These are, indeed, two separate transactions. One is an accession and the other is a loan. The items for which legal title will be transferred are the accession and receive an accession number and follow all your standard accessioning/cataloguing procedures. The group of items which the foundation wishes to retain legal title to (as the “permanent loan”) are a loan for which you should assign a number within your usual sequence of loans and write a formal agreement that has a specific time limit, which can be renewed on a regular basis (e.g., one year, renewable annually; 5 years, renewable for an additional five years; etc.). The loan agreement needs to clearly spell out what you can and cannot do with the objects (exhibit, publish, sell photographs, etc.) and what each parties’ responsibilities are (especially who is responsible for the insurance coverage and how much the items are valued at). As Ella notes, an important question to ask is whether you actually have any need (programmatic, exhibit or research) for the foundation’s objects or whether you will be, in essence, acting as an unpaid storage facility. If the latter is the case, you can chose not to have those objects at your museum or to charge the foundation an annual fee for providing the space and care.
Morals of the story: First, loans must always be set for finite periods and have written contracts/loan agreements. Second, if your museum has no use for an object, don’t agree to borrow it; you are expending your resources with no benefit to the museum (or the public it serves) and potentially increasing your liability.