There are numerous methods that can be used here:
As commented by Jens, protected switches might be used. The voltage drop is low, the current limit is typically arbitrary (wide parameter spread) and many times normal operating current, and thermal protection is integrated. When these parameters are acceptable, they are an excellent choice, and indeed, relay coils are a popular use case; they also typically provide integrated voltage clamping, meaning a clamp diode is not required.
As answered by Voltage Spike, you can use resettable fuses. But mind that, these take quite some time to open, and you need to be able to 1. source fault current for the duration, and 2. sink it through the load and switch, until it opens. It's not difficult these days to toss in a 100mΩ or lower Rds(on) MOSFET to handle such current, particularly at low voltages. Yes, some resistance is added, which will be true of every solution; you can't sense or limit current without some manner of compromise.
As the load current is tiny, you can simply make a current sink set a little bit above nominal rating, and let it open up when the load shorts out. 10mA at 24V is all of 240mW, within the ratings of even a SOT-23. A plain old two-BJT two-resistor current source circuit could be used. Note that a TVS on the common supply isn't a bad idea, to limit peak voltage (in case that's a concern; see below) and thus dissipation.
The principle extends to all manner of current limiting and switching circuits; generally, e-fuse type behavior. The current can be monitored by a control circuit, and the switch disabled, latched off either until a reset or self-resetting after a time delay (and contingent on factors like high temperature, or excess voltage). Load switch, hot-swap and wired-OR controllers, and eFuses, are available with such features, or they're not too difficult to design yourself (but it just takes a lot of parts relative to an integrated solution, and there are a number of subtle details for which a premade or integrated design is helpful).
Equally important is consideration of why failure occurs in the first place. Relay coils are just dumb balls of wire -- they don't fail on their own, but can fail due to excessive voltage or current, environmental conditions (contamination and corrosion, if not sealed, or get ruptured), or catastrophic failure of the component (say the contacts arc over and melt down the whole thing). You will have to study which of these is the greatest risk to your application.
If overvoltage is occurring, TVS diodes can be added, but keep in mind they have similar considerations to the above: if an overvoltage condition occurs with enough force (e.g. cross-wiring the 24V supply to a 48V battery, or 120VAC mains, etc.), no size TVS will withstand that amount of power, and further limiting schemes are necessary -- whether as basic as a series resistor, or a replaceable fuse, or active circuitry like a voltage limiter or load switch. Also consider inspiration from the automotive sector: load dump is a surge test that, while not unlimited in current, can deliver enough energy that for many circuits, it's best left alone -- disabling the circuit during the pulse. Circuit ideas and ICs are available for this purpose.
