Proton leak during ATP synthesis
This occurs during Oxidative phosphorylation and the &quot;proton leak&quot; process is also called Uncoupling of Oxidative Phosphorylation
The mitochondrial electron-transport chain
Electron transport, causes Complexes I, III, and IV to transport protons across the inner mitochondrial membrane from the matrix, a region of low [$\ce{H+}$] and negative electrical potential, to the intermembrane space (which is in contact with the cytosol), a region of high [$\ce{H+}$] and positive electrical potential.

Three of the four electron-transport complexes, Complexes I, III, and IV, are involved in proton translocation.
Two mechanisms have been put across that would couple the free energy of electron transport with the active transport of protons: the redox loop mechanism and the proton pump mechanism.
Uncoupling of Oxidative Phosphorylation
Electron transport (the oxidation of NADH and FADH2 by $\ce{O2}$) and oxidative phosphorylation (the synthesis of ATP) are normally tightly coupled due to the impermeability of the inner mitochondrial membrane to the passage of protons. Thus the only way for $\ce{H+}$ to re-enter the matrix is through the $\ce{F0}$ portion of the proton-translocating ATP synthase.

In the resting state, when oxidative phosphorylation is minimal, the
proton-motive force across the inner mitochondrial membrane builds up
to the extent that the free energy to pump additional protons is
greater than the electron-transport chain can muster, thereby
inhibiting further electron transport.
However, many compounds,including 2,4-dinitrophenol (DNP) and
carbonylcyanide-ptrifluoromethoxyphenylhydrazone (FCCP), have been
found to “uncouple” these processes. In a pH gradient, they bind
protons on the acidic side of the membrane, diffuse through, and
release them on the alkaline side, thereby dissipating the gradient.

The chemiosmotic hypothesis has provided a rationale for understanding the mechanism by which these uncouplers act.
Uncouplers act by dissipating the proton gradient across the inner mitochondrial membrane created by the electron-transport system.

As uncouplers, they function by carrying protons across the inner
membrane. Their tendency is to acquire protons on the cytosolic
surface of the membrane (where the proton concentration is high) and
carry them to the matrix side, thereby destroying the proton gradient
that couples electron transport and the ATP synthase.
In mitochondria treated with uncouplers, electron transport continues
and protons are driven out through the inner membrane. However, they
leak back in so rapidly via the uncouplers that ATP synthesis does not
occur. Instead, the energy released in electron transport is
dissipated as heat.

The presence in the inner mitochondrial membrane of an agent that renders it permeable to $\ce{H+}$ uncouples oxidative phosphorylation from electron transport by providing a route for the dissipation of the proton-motive force that does not require ATP synthesis. Uncoupling therefore allows electron transport to proceed unchecked even when ATP synthesis is inhibited.

Uncoupling of oxidative phosphorylation:  The proton-transporting ionophores DNP and FCCP uncouple oxidative phosphorylation from electron transport by discharging the electrochemical proton gradient generated by electron transport
References

Voet and Voet 4th ed. Biochemistry: Oxidative Phosphorylation
R.H Garret &amp; C.M Grisham Biochemistry 4th ed : Electron Transport and Oxidative phosphorylation