Reasons range from low volume and regulatory pressure to project failure or a team's disappearance. Venues typically give days to weeks of notice, halt trading at a stated time, and allow withdrawals for a further period before the asset becomes unrecoverable there.
Announced delistings tend to be brutal for price, because everyone holding on that venue must exit into a book that market makers are already abandoning. Assets delisted from several venues in succession can end up with almost no liquid market at all.
The practical obligations are unglamorous. Note the withdrawal deadline, check whether the chain is still supported for withdrawals afterwards, and be aware that tokens left on a venue past the final date have in some cases been treated as forfeited.
Related: exchange-listing-effect, market-depth-crypto, withdrawal-freeze, cex