The foreclosure laws differ from state to state. However, the standard law as applicable to Missouri is that the renters will lose their lease when the property is foreclosed. If the mortgage was recorded before the time the lease was signed, the foreclosure will end the lease. As a legality, the tenant must be given a proper written notice to evict the property. The number of days for leaving are upon the new owner's discretion. He can give as short as a 3 days notice ( which is legally the minimum time) for the renter to evict. For details see the link below:
Foreclosure

 Most renters will lose their leases upon foreclosure. The rule in most states is that if the mortgage was recorded before the lease was signed, a foreclosure will wipe out the lease (this rule is known as "first in time, first in right"). Because most leases last no longer than a year, it's all too common for the mortgage to predate the lease and destroy it upon foreclosure.

That doesn't always mean the lease-holding tenants have to leave immediately -- but those who remain join the ranks of month-to–month renters, all of whom can be terminated with proper notice, usually 30 days. And the new owners tend to move quickly to terminate, giving as little notice as is legally possible (sometimes no more than three days).

Tenants who refuse to leave face an eviction lawsuit, for which they usually have no legal defense. The impact of an eviction on a tenant's ability to find future housing can be devastating. No law prevents a future landlord from automatically rejecting tenants with evictions on their record, even when those tenants were the innocent victims of a foreclosing bank.

There are some notable exceptions, however, to this grim scenario. Tenants who participate in the federally financed Section 8 program will see their leases survive, as will tenants in New Jersey, New Hampshire, the District of Columbia, and, as of the end of November 2007, Massachusetts. In these states, new owners cannot evict lease-holding tenants unless the tenants have failed to pay the rent or violated any other important lease term or law. Tenants in other states who live in cities with rent control "just cause" eviction protection may also be protected.