I presume you mean "increase the maximum of hours for recording".
Do you already own Debut? If so, you can try unticking the "Limit recording..." box and see what happens.
On your additional query - in my experience, recordings that are not stopped 'properly', but interrupted by system restarts or program crashes, are irretrievable, kaput. I don't know of a screen-capture program that could cope with that but there may be one 
As well as Debut I use a stream downloader, and that one does finish off "recordings" in the event of a system crash, but not if the program itself becomes "not responding", which has occasionally happened since I installed it on Windows10, it was intended for Windows7. I don't know how this downloader would fare with chats.
You can download streams with Debut by selecting Network rather than Screen - that might be worth investigating via Debut Support, or maybe someone here has experience with it.

As for running out of hard disk space, that's not happened to me but I imagine that Debut would stop itself and that the recording would be viable.
Sorry I can't be more helpful.