IP-level failure protection based on the IP Fast ReRoute/Loop-Free Alternates (LFA) specification has become industrial requirement recently. The success of LFA lies in its inherent simplicity, but this comes at the expense of letting certain failure scenarios go unprotected. Realizing full failure coverage with LFA so far has only been possible through completely reengineering the network around LFA-compliant design patterns. In this paper, we show that attaining high LFA coverage is possible without any alteration to the installed IP infrastructure, by introducing a carefully designed virtual overlay on top of the physical network that provides LFAs to otherwise unprotected routers. We study the problem of how to provision the overlay to maximize LFA coverage, we find that this problem is NP-complete, and we give Integer Linear Programs to solve it. We also propose novel methods to work-around the limitations of current LFA implementations concerning Shared Risk Link Groups (SRLGs), which might be of independent interest. Our numerical evaluations suggest that router virtualization is an efficient tool for improving LFA-based resilience in real topologies.