to withdraw from a situation or to quit participating in a project or task, etc., and to thereby cause a negative consequence for someone.
We often use verbs (including phrasal verbs which this could be considered) followed by "on" to add a meaning something like "blamefully causing a negative consequence for someone or something."
For example, "She went crazy on me." Would generally mean that I was depending on her company or assistance with something, so her going crazy caused me some problem or distress.
To pull out means to depart (especially by vehicle, which I assume comes from carriages or coaches being pulled by horses, for example) or to withdraw:
- To leave or depart: The train pulls out at noon.
- To withdraw, as from a situation or commitment: After the crash, many Wall Street investors pulled out.
Since the first definition means a vehicle leaving, it would not normally be followed by on unless it meant on time or on a surface: The car pulled out on/onto the dusty road.
We can guess that it's more likely you ask about pull out on with respect to definition 2, because the three words seem to go together and in a way such that the meaning would be less obvious to many English learners.
So, to pull out on someone in this sense likely means to withdraw from a situation or to quit a project or task, etc., and to thereby cause a negative consequence for someone.
She promised to invest $2 million in our company. We spent weeks preparing plans and drafting legal agreements in preparation for that. Then she pulled out on us at the last minute. We were so disappointed.
They were engaged for three years. Then John pulled out on her on the wedding day. He just left town without telling anyone.
He promised to help me move all of my things to my new apartment, but then he called and pulled out on me, saying he was too tired from work.