They (existing lender) would not require a new policy, nor get one

Any subsequent sale or transfer, including foreclosure of junior lien, would merely be a transfer subject to the existing mortgage. Hence, the original lender's policy, with or without assignment endorsement, would be valid.

Just like a probate or trust distribution to an heir of beneficiary, that type of transfer is not an insurable sale and title insy=urance is generally not offered by commercial insurers