Let's say we have a time varying magnetic field, but that it is uniform over a region, for instance $B(x,y)=(t+2)\hat{z}$ for $x,y,z\in[-5,5]$. Since we have a changing magnetic field, there will be an accompanying induced electric field given by $\oint\vec{E}\cdot \mathrm{d}\vec{l}-\frac{\mathrm{d}\Phi_B}{\mathrm{d}t}$, where the electric field is integrated along some closed path, and $\Phi_B$ is the flux through that path. Let's take a simple example, two circles, one centered at $(1,0)$ and the other at $(-1,0)$, both with radius 1. If we draw these out though we get
Since $B$ is uniform, and they're the same path just shifted, the magnitudes of the induced fields are the same, but they give opposite directions at the origin where they meet. So from this, it appears as if different choices of loop can give wildly different values for the field at the same point, but in real life that electric field must have some value, so how is this?
In application there would be an actual wire loop in the field we could integrate along, but the induced electric field should still exist and be self consistent, even with a lack of wires.