It's most common things, If they get a better sallary/deal they will move on. Basically it's always based contract payment could be long term, weekly or monthly so once they got their weekly/monthly payment and the contract is not a long term contract. They will move on.
If the contract is long term, and they want to move on usually they will need to pay bail out before moving out.
Sponsored videos are different than if the streamer works for a casino as a brand ambassador with a long contract.
With sponsored short term contract, after finish it, streamer is free to move on. It's only his own responsibility to avoid saying something conflicts between casinos he is advertising for. It's his own respect for brands he works with in the past, now and in future.
I think that the life of a streamer is that wherever you get paid the most , that's where you go, and what the streamer has to do is get the entire Community that he manages to be interested in the casino that he is working at that moment, loyalty must be absolute for your work site, but in the casino you are working you must give them complete loyalty and in the event that you no longer work with them, you must dispense With their services in a Professional manner, since this is what the work of They, of course, the most influential and famous are the ones who Follow the most and give much more to Talk about, that is something very Logical , for example the case of Drake , who has a very large community, being a streamer he gets many People to do what he does. for him to tell or advise them, and also that his bets are too big in monetary terms, not everyone has that Capacity.
I think not streamers are not loyal to what business they are promoting not unless if they have lifetime deal with those casino. Maybe they might just give their best to promote their current clients since it can affect their credibility as a streamer if they don't give good return of service on his past clients and they are not satisfied with their service provided. If their contract end for sure they go to other casino that pays them more better also maybe after the contact ends on past clients they might delete all or some of those video contents which they are just over exaggerated on their promotions and only leave those video which is mild and not doing any harmful contents. Drake is influential guy he surely have long term contract with stake so provably he will say always good about the casino he promotes.