Lets say there is a horizontal pipe $P_1$ of diameter $d_1$, connected to another horizontal pipe $P_2$ with diameter $D_2$.
The fluid inside shall be considered as "ideal" without viscosity and flows with $v_2$ at the outlet.
The pressure at the outlet of $P_2$, $p_2$ shall be normal pressure.
Applying Bernoulli's law I get a reduced pressure $p_1$ as compared to $p_2$. By reducing $D_1$ more and more, $p_1$ is will decrease too. But then there is a point, where it would be zero or even negative. Since negative pressures are nonphysical, there must be a limit, where the assumptions behind the derivation of Bernoulli's law are not met anymore.
However, I cannot identify that point: I know, that cavitation effects will start to occur, but those are more a property of the particular fluid and in principle I could think (?) about a hypothetical fluid not subject to cavitation. So I think there must be a pitfall in the derivation of Euler's equations, from which Bernoulli's law is to be derived by integration.