If you were given free room and board in exchange for caregiving and house cleaning, do they have to give you 30 day notice if they decide they don't want you any more

Depends on where you live. Could be 5 days or 60. You need to be state specific.

Not unless they intend to go to court to evict you. Then, as noted, the amount of required written notice can vary.

As noted laws vary by area. But generally, if the room and board were part of your compensation, then they probably do not have to give you notice to vacate.

Was there a written agreement? What is the general location? Was the caregiver fired for inadequate care given? Assuming that a new caregiver is coming, this must be a very clumbsy, uncomfortable situation, maybe an impossible situation if there is not enough room for two outsiders to be there, and care can't be interrupted. If the care was inadequate, but the law requires notice anyhow, and who knows whatever other possible factors, severance pay might be a better arrangement.

Can you provide some more details?

Tell us the state. In NJ any tenant who lives there as part of their compensation must be given at least 30 days written notice to move out if their employment has ended.