The investors don’t own the trust or the mortgages, they would own the rights to the payments or income stream from the mortgages, this is why if a mortgage fails it has to be replaced and why they are called Mortgage Backed securities.
There are different arrangements
Normally the buyers of the paper (and if there are 5 transactions until they get to the final buyer - some tell me who is the buyer) has a mortgage specific pool. That means the MBS paper I buy - say at 1000 dollars (if not a principal only or interest only strip) give me the right to interest and principal on a set of numbered and identified by name mortgages
Thus when a mortgage is paid off (house sold or refinanced) - the principal flows as a lump to the buyer. In times of dropping rates the buyer might find they have 70-80% of the principal of 15-30 year regular mortgage back MBS paper returned to them in a few years
In return for assuming this form of reinvestment/interest rate risk (you do not know when you will get back your principal and how) - MBS paper (almost always rated AAA) pays a higher interest rate by say 3/8ths of a point on the 5 points then paper with a defined maturity date