If a person declares they are running for an office and starts collecting donations, what happens to that money if the person doesn’t run or quits early on?

Most states have strict laws on use and candidates have to list expenses and donations down to the penny.
Likely he spent it all but it should be public record in your state. Here it’s Missouri Ethics Commission.

They can divert the funds to another campaign after paying off expenses. But it is a system ripe for grift.

The Trumps raise funds or “campaigning” and then paid the family members huge salaries for “consulting.”

I thought I read a while back that in NY, they get to keep it. Not sure, wouldn’t swear to it. Don’t have time to google it now.

Cuomo has 18 million right now in his campaign chest. Here’s a NY Times article about what he can and cannot do with it (for example, cannot buy a car with it, can use it to finance a comeback or to donate to other candidates). If anybody can’t read it and wants to, I can cut and paste it:

https://www.nytimes.com/2021/08/12/nyregion/cuomo-campaign-18-million-spending.html

It depends on how the money was collected. If the money went to the campaign, the candidate needs to redirect it to another candidate, or to a general cause fund.
If the money went to a PAC, there is no such restriction. The candidate could buy an airplane.

The answer depends on the level of government. Candidates for federal offices are subject to some strict federal laws. If someone runs for a state or local office, the applicable state laws apply. Additionally, some bodies, such as the U.S. House of Representatives and Senate, impose their own rules in addition to the relevant law.