If you have a lot of equity in your home and a good credit rating banks will happily give you a second mortgage. If you default the bank will not lose money as they will then foreclose on the house and no taxpayer money will be lost.
The only reason the government wants to enter this market is to give loans that are not financially sound. If they default you can bet your ass the taxpayer will pick up the bill.
Even “good” second mortgages carry a lot of risk.
The reason for this is that most failures to keep up payments on second mortgages happen when the economy is in recession and people are losing their jobs.
That in turn affects the value of the original collateral.
The foreclosure would then be done by the first mortgage holder.
The second mortgage holder will be fortunate to get scraps at that point.