Subduction is a key driver of plate tectonics on Earth1. A range of observations indicate that the termination of subduction leads to diverse and unexplained tectonic and geological activity, including anomalous magmatism, exhumation and topographic subsidence, followed by rapid uplift. However, the mechanism driving this complex surface response remains enigmatic. A prime example of recent subduction termination can be found in northern Borneo (Malaysia), where subduction ceased in the late Miocene2 and was followed by a puzzling tectonic response3,4,5,6,7,8 that cannot be reconciled with our current understanding of post-subduction tectonics. Here, we use new passive-seismic data to image, in unprecedented detail, a sub-vertical lithospheric drip that developed as a Rayleigh-Taylor gravitational instability9 from the root of a volcanic arc. We use thermo-mechanical simulations to reconcile these images with time-dependent dynamical processes within the crust and underlying mantle following subduction termination. Our model predictions illustrate how significant extension from a downwelling lithospheric drip can thin the crust in an adjacent orogenic belt, facilitating lower crustal melting and possible exhumation of subcontinental material. Our study provides a new paradigm for core-complex formation in other areas of recent subduction termination.