  Establishing the presence and the nature of a quantum critical point in their
phase diagram is a central enigma of the high-temperature superconducting
cuprates. It could explain their pseudogap and strange metal phases, and
ultimately their high superconducting temperatures. Yet, while solid evidences
exist in several unconventional superconductors of ubiquitous critical
fluctuations associated to a quantum critical point, in the cuprates they
remain undetected until now. Here using symmetry-resolved electronic Raman
scattering in the cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, we report the
observation of enhanced electronic nematic fluctuations near the endpoint of
the pseudogap phase. While our data hint at the possible presence of an
incipient nematic quantum critical point, the doping dependence of the nematic
fluctuations deviates significantly from a canonical quantum critical scenario.
The observed nematic instability rather appears to be tied to the presence of a
van Hove singularity in the band structure.
