Gaining Secret Interim, but then contract position isn't available

What happens in this scenario -
Applicant is sponsored for Secret Clearance for a contract position with company A, and the process begins.
Interim clearance is granted, but position is then no longer available.

Applicant is offered a contract (or full time) job by company B that requires at least interim clearance for same level (Secret) to begin work within the same agency.

Does the investigation process begin again or can the existing investigation continue while applicant begins work?

The existing investigation can be picked up by the new company, if they do it correctly. If they are not sure, I understand that the JPAS helpdesk is very helpful.

The interim clearance MAY be a different story. I suspect that the new employer will have to request it and it may, again, take several weeks if it is granted at all.