The evaluation of reliability for interconnection networks is of utmost importance in the design of systems. When it comes to assessing the reliability of such networks, two key metric parameters are extra connectivity and extra diagnosability. Most prior studies on extra connectivity and extra diagnosability focus on specific networks, yet characterizing the reliability of general regular networks is more valuable. Guo and Ekinci recently proposed folded hypercube-like networks, encompassing the folded hypercube (FH) and folded crossed cube (FCC). This paper aims to develop a general approach to investigate the extra connectivity and extra diagnosability of folded hypercube-like networks. The research outcomes will be directly applied to the FH and FCC.