Is there an example of a bond with negative bond enthalpy?
Bond enthalpy is like a measure that tells us how strong/stable a particular bond is.
Definition:

Bond enthalpy (also known as bond energy) is defined as the amount of energy required to break one mole of the stated bond.


To break a bond, energy must be provided to the bond. How is that energy provided?

The reactants are either heated or they take up energy from the surroundings, that is, they take in energy in the form of heat from the surroundings, overcome their bond enthalpies and break the bond.
All bonds require energy to be broken.
A negative Bond enthalpy simply means that the bond is highly unstable and would not exist in the first place.
I highly doubt if any compound has negative bond enthalpy.{Not even Dimeric Helium}
From Wikipedia:

Based on molecular orbital theory, $\ce{He2}$ should not exist, and a chemical bond cannot form between the atoms. However, the van der Waals force exists between helium atoms as shown by the existence of liquid helium, and at a certain range of distances between atoms the attraction exceeds the repulsion. So a molecule composed of two helium atoms bound by the van der Waals force can exist.The existence of this molecule was proposed as early as 1930.