Vague question, Snikers.
For one thing, are you talking about turbine bearings or, say, pump bearings.
Would you mean: lost 100% of oil pressure to all turbine bearings instantaneously? Physically impossible, so let's ignore it.
Would you mean: slowly lost oil pressure over a manageble period of time to some turbine bearing. One would hope the crew would be alerted and shut the engine down, for if it continued running then serious damage is very likely to ensue.
Or would you mean: lost some/most oil pressure over X period of time to various bearings Y,Z,W? Then we would want to know what engine you are talking about, what X is, and which bearings Y,Z,W you are concerned about.
There are, definitively, no shutdown mechanisms on any engine which trigger in all of the possible cases of bearing oil-pressure loss (that is, for all X, Y, Z, W).