Cash for keys is generally a negotiated payment to the owner - occupant as an incentive to vacate the premises in an orderly fashion by a given date. The payment amount in my experience has been from 1 - 2 months of rental value or monthly cost. That is not an absolute and can vary as it is a negotiation. It is all dependent on the circumstances and what value the lender puts on a negotiated settlement time as opposed to litigation. You may want to consult with an attorney as it should not be an expensive proposition.
This is not meant as legal advice and you should consult with an attorney in your State.
WA foreclosures of property occupied by a "bona fide" tenant are subject to P.L. 111-22, which provides that the new incoming owner has to give 90 day's notice to the tenants before commencing an eviction.
If you are caretaking a person with disabilities, you can also invoke the ADA and/or the WLAD to request reasonable accommodation. If the new owner declines, call the media.
Cash for keys is a way to work around the 111-22 restrictions. You are under no obligation to assent to this if you do not want to, as this is a purely private agreement. If you choose the cash for keys option, negotiate to get the payment in two portions, so you have cash to move and an incentive to leave on time and with the property tidy.
Also, you'd benefit from a consult with the NW Justice to see if this property can be salvaged from foreclosure. The Bar has a free project to match volunteer attorneys with homeowners needing assistance. The information is on the top of the homepage at http://www.wsba.org
Hope this helps. Elizabeth Powell