Clipping distortion is a common problem when the amplitude of input signals exceeds the desired region of an analog-to-digital converter. Unlimited Sensing Framework (USF) alleviates the clipping distortion by folding out-of-range signals into a within-range via modulo operations. Instead of the infinitesimal assumption, a residual-remainder coupled USF is proposed to eliminate the remainder sampling error by coupling the residual sampling component. The proposed framework does not only relax the oversampling rate in the original USF to approaching the Nyquist sampling rate, but also provides a more accurate signal recovery capability.