I am aware that similar questions have been asked countless times, but I have not been able so far to find an appropriate match for my case.
I am running a 32-bit, 14.04 server within an OpenVZ container, which provides this kernel:
$ uname -r
2.6.32-042stab116.2
Not sure how/why it started, but apt has been repeatedly trying (and failing) to upgrade to the 3.13 series, ending up like this:
$ dpkg -l |grep linux
ii libselinux1:i386 2.2.2-1ubuntu0.1 i386 SELinux runtime shared libraries
ii linux-firmware 1.127.22 all Firmware for Linux kernel drivers
ii linux-headers-3.13.0-100 3.13.0-100.147 all Header files related to Linux kernel version 3.13.0
ii linux-headers-3.13.0-100-generic 3.13.0-100.147 i386 Linux kernel headers for version 3.13.0 on 32 bit x86 SMP
ii linux-headers-3.13.0-101 3.13.0-101.148 all Header files related to Linux kernel version 3.13.0
ii linux-headers-3.13.0-101-generic 3.13.0-101.148 i386 Linux kernel headers for version 3.13.0 on 32 bit x86 SMP
ii linux-headers-3.13.0-91 3.13.0-91.138 all Header files related to Linux kernel version 3.13.0
ii linux-headers-3.13.0-91-generic 3.13.0-91.138 i386 Linux kernel headers for version 3.13.0 on 32 bit x86 SMP
ii linux-headers-3.13.0-92 3.13.0-92.139 all Header files related to Linux kernel version 3.13.0
ii linux-headers-3.13.0-92-generic 3.13.0-92.139 i386 Linux kernel headers for version 3.13.0 on 32 bit x86 SMP
ii linux-headers-3.13.0-93 3.13.0-93.140 all Header files related to Linux kernel version 3.13.0
ii linux-headers-3.13.0-93-generic 3.13.0-93.140 i386 Linux kernel headers for version 3.13.0 on 32 bit x86 SMP
ii linux-headers-3.13.0-96 3.13.0-96.143 all Header files related to Linux kernel version 3.13.0
ii linux-headers-3.13.0-96-generic 3.13.0-96.143 i386 Linux kernel headers for version 3.13.0 on 32 bit x86 SMP
iF linux-image-3.13.0-92-generic 3.13.0-92.139 i386 Linux kernel image for version 3.13.0 on 32 bit x86 SMP
iF linux-image-3.13.0-93-generic 3.13.0-93.140 i386 Linux kernel image for version 3.13.0 on 32 bit x86 SMP
iF linux-image-3.13.0-96-generic 3.13.0-96.143 i386 Linux kernel image for version 3.13.0 on 32 bit x86 SMP
rH linux-image-extra-3.13.0-100-generic 3.13.0-100.147 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
rH linux-image-extra-3.13.0-101-generic 3.13.0-101.148 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
rH linux-image-extra-3.13.0-92-generic 3.13.0-92.139 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
iU linux-image-extra-3.13.0-93-generic 3.13.0-93.140 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
iU linux-image-extra-3.13.0-96-generic 3.13.0-96.143 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
ii linux-libc-dev:i386 3.13.0-101.148 i386 Linux Kernel Headers for development
ii syslinux 3:4.05+dfsg-6+deb8u1 i386 collection of boot loaders
ii syslinux-common 3:4.05+dfsg-6+deb8u1 all collection of boot loaders (common files)
ii util-linux 2.20.1-5.1ubuntu20.7 i386 Miscellaneous system utilities
My understanding is that the kernel is entirely under the OpenVZ host's responsibility, and I have been advised to simply get rid of all these images, which are ignored by the system anyway. However, all my attempts to completely remove the packages have failed with various error messages.
This is what happened when I tried to explicitly purge all unwanted linux* packages.
Using aptitude instead of apt-get got rid of a a few packages and changed the status of all remaining images to pH, but did not resolve the problem:
$ dpkg -l |grep linux
ii libselinux1:i386 2.2.2-1ubuntu0.1 i386 SELinux runtime shared libraries
ii linux-firmware 1.127.22 all Firmware for Linux kernel drivers
ii linux-headers-3.13.0-100 3.13.0-100.147 all Header files related to Linux kernel version 3.13.0
ii linux-headers-3.13.0-100-generic 3.13.0-100.147 i386 Linux kernel headers for version 3.13.0 on 32 bit x86 SMP
ii linux-headers-3.13.0-91 3.13.0-91.138 all Header files related to Linux kernel version 3.13.0
ii linux-headers-3.13.0-91-generic 3.13.0-91.138 i386 Linux kernel headers for version 3.13.0 on 32 bit x86 SMP
ii linux-headers-3.13.0-92 3.13.0-92.139 all Header files related to Linux kernel version 3.13.0
ii linux-headers-3.13.0-92-generic 3.13.0-92.139 i386 Linux kernel headers for version 3.13.0 on 32 bit x86 SMP
ii linux-headers-3.13.0-93 3.13.0-93.140 all Header files related to Linux kernel version 3.13.0
ii linux-headers-3.13.0-93-generic 3.13.0-93.140 i386 Linux kernel headers for version 3.13.0 on 32 bit x86 SMP
ii linux-headers-3.13.0-96 3.13.0-96.143 all Header files related to Linux kernel version 3.13.0
ii linux-headers-3.13.0-96-generic 3.13.0-96.143 i386 Linux kernel headers for version 3.13.0 on 32 bit x86 SMP
pH linux-image-extra-3.13.0-100-generic 3.13.0-100.147 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
pH linux-image-extra-3.13.0-101-generic 3.13.0-101.148 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
pH linux-image-extra-3.13.0-92-generic 3.13.0-92.139 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
pH linux-image-extra-3.13.0-93-generic 3.13.0-93.140 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
pH linux-image-extra-3.13.0-96-generic 3.13.0-96.143 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
ii linux-libc-dev:i386 3.13.0-101.148 i386 Linux Kernel Headers for development
ii syslinux 3:4.05+dfsg-6+deb8u1 i386 collection of boot loaders
ii syslinux-common 3:4.05+dfsg-6+deb8u1 all collection of boot loaders (common files)
ii util-linux 2.20.1-5.1ubuntu20.7 i386 Miscellaneous system utilities
I ran aptitude again on the above list of 3.13 packages, and this time all headers were gone, but the "extra" images are still there.
$ dpkg -l |grep linux
pH linux-image-extra-3.13.0-100-generic 3.13.0-100.147 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
pH linux-image-extra-3.13.0-101-generic 3.13.0-101.148 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
pH linux-image-extra-3.13.0-92-generic 3.13.0-92.139 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
pH linux-image-extra-3.13.0-93-generic 3.13.0-93.140 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
pH linux-image-extra-3.13.0-96-generic 3.13.0-96.143 i386 Linux kernel extra modules for version 3.13.0 on 32 bit x86 SMP
[...]
I gave it yet another go, and this is the output. It looks as though in order to purge these extra images (with obvious unmet dependencies, since the corresponding images are gone) some files required by aptitude are missing:
depmod: FATAL: could not load /boot/System.map-3.13.0-100-generic: No such file or directory