Change chain with cassette or do nothing? Sometimes as a hobby I repair entry level bikes for myself or for friends and family.
The rear derailleur is working fine (no skipping/ slipping etc..).
But than I discover (with a chain checker), that the chain need to be replaced (almost 1.0 by a Park Tool CC-2). I changed the chain slipping / skipping appears.
The conclusion: probably the cassette  also needs to be replaced. So by replacing the chain only, it doesn't improve the situation or even makes it worse.
My question is, in such situation (old entry level bike etc..), if the rear derailleur works fine, is it worth it to replace the chain?
If I leave on an old chain and the cassette is most probably already very worn, can the old chain provide any additional problems?
If chain wear is beyond 1% then you are probably looking at a new drivetrain including chainrings. I would just remount the old chain and get the full wear out of everything else.
As far as changing chain only the industry standard is wear between 0.5-0.75% if you change within this range the theory is you will prolong the life of the drivetrain and perhaps never have to change anything except the chain.
The likelihood of snapping a chain is not very high for normal everyday use.