There seems to be two separate question here:
Should one do this?
Not under most circumstances. Modifying third party extensions de-facto forks it with all implications of future maintenance and/or merging upstream (from original) changes.
Without long term commitment it’s just not practical and promptly falls apart, like in the cases you witnessed.
Should one get involved with this?
There are several possibilities here:
- Fix outstanding issue in modified plugin. This gets rid of immediate problem, but essentially just digs client’s site deeper into the hole.
- Extract the custom changes and make them work properly with original plugin without update issues. This is about optimal, but can be harder to sell than previous option.
- Commit to the proper maintenance of the fork. This is very unlikely, unless you will be with the client for a lot of time (and money :).
From here it’s more business than technical. It is your decision if you enjoy this kind of work. It is client decision what they want to do with their site in the end.