Low-Side Current Sense Simulation

This circuit is not well "biased" as already pointed.

You should add a resistor between +10 V and (+)input.

This resistance will make the "sensor" act in the positive and negative input.

I should add also the Stability Bode diagrams (Nyquist test).

With this resistor (and adjusting some others), this circuit should be ok (to be tested).
Don't forget the decoupling capacitor on power supply opamp.

With a very small amplitude as you have used (100uV), it is operated right at the bottom of the common mode input capabilities of the opamp. In this case that is given as 0V, so that should be OK.

I have just supplied the opamp with a dual supply and the result are as shown below. You could also add a DC offset to the output, so the opamp can output correctly. This DC offset can also be a voltage that together with the gain is in the middle of the opamp supply voltage. The DC offset will anyway be removed by the lowpass filter at the output.

Without adding any additional bias and making sure the input is always positive, the output is as given

The two inputs (A and B below) of your differential amplifier are at 0V, their difference is zero, and so the output of the system should be 0V at DC. Since the negative supply for your op-amp is ground also, at DC this op-amp is saturated against its own negative supply. The situation resembles this:

^{simulate this circuit – Schematic created using CircuitLab}

While saturated, this op-amp's open-loop gain drops to near zero, because its output cannot move from 0V, which is why you see negative hundreds of dB closed-loop gain.

While you may have intended to use 0V (ground) as the op-amp's negative supply, which might be a perfectly acceptable possible real-life condition, an AC analysis cannot be performed in this DC state, because the op-amp is no longer behaving as it would if it were not saturated.

You could adjust DC input levels to shift the output above ground, which would "release" the op-amp and yield a bode plot with expected and correct closed-loop gain, but the simplest solution seems to be to temporarily give the op-amp a proper negative supply:

^{simulate this circuit}

That permits the 0V output state to lie well away from saturation, so these DC test conditions are no longer "exceptional". The AC analysis can then proceed using the op-amp's usual ridiculously large open-loop gain, and you would see the expected 29dB closed-loop gain near DC.

If you insist on testing frequency response using ground as the op-amp's negative supply, then you must bias the inputs in such a way as to raise the DC (quiescent) output well above ground (out of saturation), and simultaneously ensure that its inverting and non-inverting inputs also lie well within the op-amp's acceptable input voltage range. You might do something like this:

^{simulate this circuit}

V2 will raise both input potentials, to set their common mode value well into a region where the op-amp is happy, while V1 applies a small difference between them to raise the op-amp's output out of saturation. You then use V1 as your modulated source for an AC analysis.