There were very serious shailos after the war about granting a woman the right to remarry in the absence of firm proof that the husband had died.
Unfortunately, there were cases where the first husband reappeared a number of years later. The children of the 2nd husband are 100% mamzeirim. i know of such a case and this family had to marry off all their kids to out of towners. The local community did not publicize this fact but they definitely did not marry any of their children to this family. Whether or not this fact had to be disclosed voluntarily in a potential shidduch has always been something I never got a clear answer to.