In South Dakota an attorney for adults sexually abused as children by priests and nuns contended that the state legislature passed a statute of limitations (in approximately 2010) preventing lawsuits and/or prosecution for such crimes and thereby rescued the alleged perpetrators from accountability. That's what I have tentatively labelled a bill of “anti”-attainder. So, is this allowable generally, or do precedents or custom require extensions of statute of limitations to take effect much later, after any current victims are likely to be dead, as a guarantee to those victims of due process if they come forward? Because it seems to me the legislature could otherwise be bribed to protect perpetrators ex post facto.
A Bill of Attainder, as described in this question is a legislative act which declares a person guilty of a crime, without a judicial trial. Therefore, an "anti-Attainder" would logically be a legislative act which declares a person not guilty of a crime, without a trial or overruling the outcome of a trial. As a comment mentions, this is more often known as a "legislative pardon". In most US states the pardoning power is given to the Governor, in some cases together with a "Board of Pardons' or "Board of Parole". Legislative pardons are rare, and in some states are not allowed.
Changing the statute of limitations on a crime does not affect only a particular named person or people, but rather anyone accused of that crime. The legislature may (if it so chooses) shorten the statute period at any time, and the shortened time period will affect anyone against whom formal charges have not yet been filed. The legislature may also lengthen the period. I believe that such changes also take effect for anyone not yet charged, but an argument might be made that as applied to someone accused of committing the crime before the extension was passed, the is an ex post facto law. I don't know of any court decision so holding.
The legislature may also at any time repeal the law making some act a crime. In such a case, anyone not yet charged could not be charged in future. I am not sure if people already charged, or even with trials in progress when the repeal is effective, would be entitled to a dismissal as of right, but I think there normally would be a dismissal as a policy matter. Look at recent repeals of laws criminalizing possession of certain quantities of marijuana in some US states as examples.
In such matters the legislature acts on whatever basis it sees fit. Political pressure is probably more likely than true bribery, but corrupt legislatures are not unknown. On the other hand, pressure to repeal or modify a law seen as unjust or overly harsh can lead to legislative actions. In any case, this is a political matter of legislative choice.