The success of full-stack full-duplex communication systems depends on how effectively one can achieve digital self-interference cancellation (SIC). Towards this end, in this paper, we consider unlimited sensing framework (USF) enabled full-duplex system. We show that by injecting folding non-linearities in the sensing pipeline, one can not only suppress self-interference but also recover the signal of interest (SoI). This approach leads to novel design of the receiver architecture that is complemented by a modulo-domain channel estimation method. Numerical experiments show that the USF enabled receiver structure can achieve up to 40 dB digital SIC by using as few as 4-bits per sample. Our method outperforms the previous approach based on adaptive filters when it comes to SoI reconstruction, detection, and digital SIC performance.