Three structures exist. The client owns the account and grants access. Your agency owns it in your MCC. Or the fulfillment vendor owns it in theirs. Only the third one is a trap, and it is more common than it should be.
If the vendor owns the account, your client historical data lives with a company your client has never heard of. When the relationship ends, you are negotiating for access to performance history you paid to create. Some vendors will transfer it cleanly. Some will not, and there is no mechanism to make them.
Client-owned is the cleanest structure and the hardest to sell to clients, who do not want another login. Agency-owned in your MCC is the practical middle: you control access, the client can be granted view rights, and a vendor change does not touch the account.
Whichever you pick, put the offboarding mechanism in the agreement — who transfers what, within how many days, in what condition. The time to negotiate that is when everyone is happy.