An original appraisal was given, and the appraised value decreases monthly. Every month, the banks withdraw from that. If after 20 years, there is nothing left to withdraw, can I be kicked out of my house?
No. They cannot kick you out. The worst thing that can happen is that they can say you have no more equity that you can access from this house anymore. As you grow older, the amount of equity, and the percentage you can access grows. But they can never kick you out of the house so long as you are living there. This government program was initiated in order to allow seniors to access their home equity without jeopardizing their right to be able to live there.
The other end of the spectrum is that if you pass away and the value of your house is down. If the amount you have taken out over your lifetime exceeds the value of the house, you will still be covered by PMI insurance. This protects your children and your family from having to step in and take care of it.