Abstract The single degenerate (SD) model, one of the leading models for the progenitors of Type Ia supernovae (SNe Ia), predicts that there should be binary companions that survive the supernova explosion, which, in principle, should be detectable in the Galaxy. The discovery of such surviving companions could therefore provide conclusive support for the SD model. Several years ago, a new type of mysterious variable was discovered, the so-called blue large-amplitude pulsators (BLAPs). Here we show that all the properties of BLAPs can be reasonably well reproduced if they are indeed such surviving companions, in contrast to other proposed channels. This suggests that BLAPs could potentially be the long-sought surviving companions of SNe Ia. Our model also predicts a new channel for forming single hot subdwarf stars, consistent with a small group in the present sample of hot subdwarf stars.