I am writing this post after weirdly finding my own router quite literally disintegrating.
We start this post by saying it isn't melting, at least due to heat, the "melted" part of the router is gooey like rubber and seems to be spreading across the bottom of the router. This router sits in an untouched area where chemicals or anything else shouldn't be able to affect (the bottom of) the router. It has been active for somewhere between 6-12 months and has had some buggy behavior lately but I think that would be the terrible firmware and not due to this. The router was working up until I unplugged it to look at it, so nothing show stopping is occurring but it is an ugly mess.
With some research I didn't find my router having this issue However I did find other Netgear routers possibly doing this. A quote from the Netgear Community
This seems nearly exactly what I am experiencing, a really sticky hard to clean substance and I do live in NC so we have a fair bit of humidity. BUT it does seem only the exteriors were getting sticky and not fully desintegrating. If anyone is able to find something closer to my issue please contact [email protected]