Legal Question in Landlord & Tenant Law in California

Your having lost the agreement does not invalidate it, but it makes it difficult to prove the agreement's terms. If you and your tenant disagree on what is contained in the agreement, then, in a legal action, the court would need to decide on the terms.

The tenant's occupying the premises and paying rent implies that there is an agreement, but, by itself, the situation does not prove the nature of the $400 that is in dispute. If a legal action arises, the plaintiff will generally have the burden of proving the nature of the money, by the circumstances. For example, if the tenant paid one sum, the first month and then paid $400 more, in the subsequent months, it is reasonable to conclude that the initial $400 was part of a rental payment.

You should note that, if the $400 was in security for rent, then it is subject to the rules about security deposits, regardless of what the contract called the deposit. Some landlords call such deposits "ernest money" or "initial deposit" or "account setup fee" or other phrases. If the money was deposited as a way for the landlord to pay rent, if the tenant doesn't pay, then the deposit is a security deposit and cannot be nonrefundable.

I'm wondering what it really matters. If it was to be applied to rent, then the tenant gets to keep $400. Why would they want to pay you an extra $400 and then get it back? It doesn't make sense.