In the Ramsey model, $K_t$ denotes capital, and $A_t$ denotes the assets/wealth of the households.
However, each household is identical. Since the economy is closed, the assets of each household equal their share of the capital. So, $A_t = K_t/H$, where $H$ is the number of households.
However, in theory, $A_t$ can be negative. Obviously a household can accumulate debt at some point in their lifetime. But $K_t/H$ can never be negative, since $K_t$ itself, total capital in the economy, cannot be negative.
So I do not understand how it makes sense in the Ramsey model to talk about "wealth" and "borrowing" and "debt" since $A_t$ is forced to be positive?