There are often verbs which are both seperable and inseperable at the same time (often with prefixes like über). One verb conjugator gives a seperate conjugation of beigeben listing it as inseparable for subordinate clauses and seperable in main clauses. Is this a rule I haven't encountered yet? Scanning google did not offer an explanation based on my search guesses. Does that ever determine which to use when the verbs are listed as both separable and inseparable?
There are cases of verbs which seem to behave sometimes as separable and sometimes as not separable. However, these variants always differ in their primary stress. Examples:
umfahren = to drive around s.o.
umfahren = to knock s.o. down with a vehicle
übergehen = to pass s.o. over (e.g. for promotion)
übergehen = to turn into (e.g. argument into violence)
In all such cases, the meaning and stress pattern determines the behaviour. The separable variant always behaves as a separable verb and vice versa.
Note that "beigeben" is not one of these ambiguous forms: it is always a separable verb. (In fact, there are no non-separable verbs with the prefix "bei-" at all.) It's just that even separable verbs exhibit separation in some but not all forms.