Alice files a lawsuit against Bob
This is a civil suit, it will not lead to any court punishing Alice, or anyone else. If facts come out showing that Alice violated the law, the local prosecutor could, but need not, file a criminal case against Alice. If the prosecutor does not file such a case, Alice's worst possible outcome is to get no damages, with costs and fees awarded to Bob (or his estate).
If Bob dies and Alice wishes to drop the case, there is no obvious reason not to permit it, unless Bob or his estate has counter-sued. Bob (or his estate) might ask for costs and legal fees, and perhaps sanctions for a frivolous suit. The court might well asses whether to grand such a costs order before or as it dismisses the case. ;
The question seems to confuse the idea of a civil lawsuit and that of a criminal prosecution. In an Civil lawsuit, one person (or company) (the plaintiff) claims that another (or several others) (the defendant) have violated an agreement, or have in some other way caused legal injury. For example, if Alice claims that she had a contract with Bob and Bob violated the terms that would be a civil suit. Or if Alice claims that Bob infringed her copyright, or slandered her, or falsely advertised something or any of many other possible situations. The case would be Alice C vs Bob D.
However, if Alice accuses Bob of having stolen from her, or punched her, or raped her, that woulds be a criminal accusation. The police would investigate, and if they found evidence to support the accusation, the local prosecutor could (but need not) file a case, which would be something like State of Franklin vs Bob D IN THE CRIMINAL COURT. Alice would be a witness, but not the plaintiff. If the investigation found that Alice committed a crime also, the prosecutor might file, State of Franklin vs Alice C Or the prosecutor might file both cases, or neither. The prosecutor has wide discretion whether or not to prosecute in any particular case, even when the evidence is clear. Neither Alice nor Bob could insist that either criminal case be dropped. Only the prosecutor, or the Judge, could do that.
A criminal court is a different court from a civil court, and in many places a given judge hears only one or the other type of case. In many other places a judge may hear both kinds, but any one case is still either civil or criminal.