Your text may be translated as:

“notwithstanding any civil or criminal actions to which the Company may be entitled” (or)

“notwithstanding any civil or criminal actions that the Company may be entitled to bring”

In legal contexts “asistir” often has the specific meaning of “to have the right to” or “to be entitled to.” Here are some examples:

Le asiste el derecho a examinar el expediente (“you have the right to examine the case file”)

Le asiste el derecho a alegar por escrito lo que en su defensa estime conveniente (“you have the right to submit written allegations in your defense”)

Le asiste el derecho de reclamación ante la Junta Arbitral de Consumo (“you have the right to file a complaint with the Consumer Arbitration Board”).

In your text there is actually an ellipsis, and what is implied is “…sin perjuicio del derecho a entablar las acciones civiles o penales que le asiste a la Compañía.” This is what the lawyer who drafted your text was thinking and that's why "asiste" was in the singular rather than in the plural ("le asiste el derecho a..."). Lawyers often do this and it can really confuse translators! Hope this helps.