A closed loop linear system is unstable if some Laplace s with positive real part makes the denominator of the transfer function zero, but the nominator is non-zero. We say there's pole in the right half plane. The system starts to oscillate with exponentially growing amplitude. The imaginary part of the pole determines the frequency. The bode plot, when done accurately enough, can predict the existence of a right half plane pole although it doesn't show its place. Search for Nyquist stability criteria to learn more of it.
There's also possible the limit case - a pole of closed loop transfer function just on the imaginary axis i.e. the gain becomes infinite at a certain frequency. The system may oscillate sinusoidally in that frequency if some impulse input or state variable initial value starts the oscillation. In practice such thing never happens exactly, but you searched only for it and ignored the exponentially growing oscillations.
ADD due the comment:
You said your process G has phase margin -37 degrees. It has no phase margin at all. Phase margin tells how much there's room to insert more phase lag before the phase lag grows to 180 degrees assuming the absolute value of G is =1. This is how a control engineer thinks it. He empirically assumes that if there's no phase margin just like in your case, there's a good change to exist an exponentially growing sine which is amplified infinitely in your closed loop with transfer function G/(1+G).
That assumption can be wrong in certain cases. Nyquist showed what's the exact procedure to check the stability by inspecting the transfer function only at imaginary s-values. You may even find a ready to use Nyquist plot function from your programs. It's freely available online for ex. in this website: https://mathlets.org/mathlets/bode-and-nyquist-plots/
The system is stable or it's not stable. Thinking it's stable at some frequencies and it's unstable at some other frequencies is your own way to use the term stability. It's like you could say that a woman is pregnant every day at 13:05 o'clock but she's not pregnant at other times.
BTW. Nyquist developed his stability criteria when no computers were available. There was no practical way to simulate the closed loop behaviour of complex transfer functions nor to find the poles of the closed loop system.