Only tax lien foreclosures and HOA lien foreclosures can be redeemed.
For homesteads there is a period 2 years unless a court evicts the occupants.
For investment properties the period is 6 months.
A mortgage foreclosure changes ownership immediately and without redemption. If the second mortgagee forecloses, for example, the owner is no longer in title.
If the owner continues to occupy the property after foreclosure, the new owner can evict them.
The second mortgagee must continue to make payments to the first mortgagee, but the first mortgagee can foreclose anyway, taking the property from the second mortgagee.
If the first mortgagee forecloses, the second mortgagee is just out of luck. The second lien no longer exists against the property.
Remember most mortgage notes contain language that the property serves as collateral, but the borrower is personally liable for the unpaid balance.