Yes. But it is also true that many of these programs do not. Either because they recapture too small a share of price appreciation, because they don’t have a clear mechanism for reinvesting the recaptured equity or because they use recaptured funds for some other purpose entirely, many loan programs fail to replace affordable units that are sold. While any shared equity program can occasionally require additional subsidy to maintain affordability, many of the existing shared appreciation loan programs have selected equity sharing formulas that are likely to require some level of additional public investment when prices are rising rapidly.
Nonetheless, many shared appreciation loan programs have very effectively built growing portfolios of affordable homes and maintained that affordability between buyers. In some cases, the loan program sponsor retains a right of first refusal which enables them to identify a new lower income buyer for the same house and they are able to reinvest the proceeds from the repayment of the loan to assist the second buyer. In this way they can function similarly to a deed restriction program but under a different legal structure.