A classical example is Schmitt-Grohe/Uribe’s (2003) paper on closing small open economy models. There is a unit root in the net foreign asset position if interest rates are constant/do not react to asset positions. Solutions in their case were to have a debt elastic interest premium or an endogenous discount factor. In closed economy models you can generate something similar by having a borrowing constraint where the Lagrange multiplier on the constraint increases in debt and therefore creates a “utility premium”.