Recent hydrodynamical simulations of the late stages of supernova remnant (SNR) evolution have revealed that as they merge with the ambient medium, SNRs implode, leading to the formation of dense clouds in their center. While being highly chemically enriched by their host SNR, these clouds appear to have similar properties as giant molecular clouds, which are believed to be the main site of star formation. Here, we develop a simple model in order to estimate the efficiency of the star formation that might be triggered by the implosion of SNRs. We separately consider two cases: cyclic star formation, maintained by the episodic driving of feedback from new generations of stars, and a single burst of star formation, triggered by a single explosion. We find that in the cyclic case, star formation is inefficient, with implosion-triggered star formation contributing a few percent of the observed star formation efficiency per freefall timescale. In the single-burst case, higher star formation efficiencies can be obtained. However, while the implosion-triggered process might not contribute much to the overall star formation, due to the high chemical enrichment of the birth clouds, it can explain the formation of a significant fraction of metal-rich stars.