The answer is, it depends.
In the first scenario, if you quit, and I’m talking from my understanding of Minnesota employment law and making an assumption that it’s very similar in most other states, that if you quit “for cause”, yes, you can get unemployment. Let’s say they change you from a day shift to a night shift, or cut your hours in half, or create some sort of hostile work environment, that makes you have a legitimate grievance that can not be solved unless you quit, then that is “for cause”, and you can usually get unemployment. There are usually very well defined sets of circumstances that you can find online, just look up the unemployment area on your state’s website and you should be able to figure out if the reason you want to quit is “just cause” (but if you just can’t stand being there anymore, then no, it’s not just cause”.
Regarding being terminated for poor performance, usually it has to be a justified firing…they have to have cause to fire you AND deny you unemployment benefits. If they just didn’t think you were doing a good enough job, it’s questionable whether or not they can deny you benefits.
But, and this is from an insider perspective, being the person in charge for some former employers of deciding whether or not to object to someone’s filing, what happens is this. The person will file for benefits and the state will ask them the circumstances regarding the termination of employment. Then a letter is sent to the employer to verify the information given. If you said on your application that you were laid off or quit for cause or what not, and your employer knows they fired your ass for gross incompetence, or you came in one day and told your boss to suck it, then they might well fill that form out and return it. But basically, being insurance, what this impacts for an employer is a very small portion of their tax liability. If they have a lot of layoffs their premium might go up, but it’s not a huge cost, and a lot of employers might not even bother to fill that form out. Even if the employer knows you shouldn’t get unemployment based on what happened, they might be decent enough to just trash the form and never send it back. But the point is, they are within their legal rights to seek to deny you unemployment, but ultimately, it’s the state’s decision, not the employer’s.