Some brands of audio tape was prone to the binder becoming hygroscopic, softening and gumming up the heads and tape path thus destroying the tape as it was being played. It is well known in pro audio circles that Ampex 456 was especially prone to this, but I have found other brands exhibiting this issue too.
I was approached about 18 years ago to digitize hundreds of hours of archival reel to reel tape. To properly recover the recordings, I built a low temperature convection oven that would heat the tapes to around 100F with circulating air for about 5 days. This treatment was very successful, and I was able to recover the recorded material in very good condition.
Cassettes could be treated the same, however the cassette shell will prevent positive air circulation around the tape inside. If the shell can be opened (many are held together with small self tapping screws) the tape reels could wrapped in tissue paper, hung on a small diameter wood dowel, and allowed to dry in the heat cabinet. Once dried out, they could be re-assembled into the shells and immediately played.