A timely and well-managed phase-out of bank lending to the fossil fuel sector is critical if Paris climate targets are to remain within reach. Using a systems lens to explore over $7 trillion of syndicated fossil fuel debt, we show that syndicated debt markets are resilient to uncoordinated phase-out scenarios without regulatory limits on banks’ fossil fuel lending. However, with regulation in place, a tipping point emerges as banks sequentially exit the sector and phase-out becomes efficient. The timing of this tipping point depends critically on the stringency of regulatory rules. It is reached sooner in scenarios where systemically important banks lead the phase-out and is delayed without regional coordination, particularly between US, Canadian and Japanese banks.