Typically, sample size determinations are done to ensure a reasonable probability of rejection given the null hypothesis in false in a certain way (with an effect of a certain size).

It is prudent to try to plan a study with large enough sample that it will likely meet its objectives.

However, after you have data---even if not as much as you had projected---if you get a significant result, then that result stands on its own. Maybe the effect is larger than expected, the sample variance is lower than expected, or whatever. Just check assumptions to make sure the 'significant' result was produced by a valid test procedure.

A sample size that's a little low doesn't invalidate the findings of the study.

Typically, sample size determinations are done to ensure a reasonable probability of rejection given the null hypothesis is false in a certain way (with an effect of a certain size).

It is prudent to try to plan a study with large enough sample that it will likely meet its objectives.

However, after you have data---even if not as much as you had projected---if you get a significant result, then that result stands on its own. Maybe the effect is larger than expected, the sample variance is lower than expected, or whatever. Just check assumptions to make sure the 'significant' result was produced by a valid test procedure.

A sample size that's a little low doesn't invalidate the findings of the study.