I'd think it more likely that the Citadel Council would crash Benezia's accounts due to her association with a terrorist, though it's possible Liara would inherit her money provided it wasn't tied up in legal red tape for years to come.
In any case, part of why her transition to her new ME2 role comes across as contrived is because she's specifically depicted as naive and socially isolated to the point of barely being able to navigate a conversation in ME1 - suddenly she's supposed to be socially savvy enough to survive, let alone excel, in the world of professional espionage? Going from having her nose stuck in a book at an isolated dig site to networking, making and maintaining contacts? Knowing who to trust, who to pay off, who to cut loose, who to kill, how to garner and maintain loyalty? No transition is depicted save for her doing a wiki-walk to learn Shepard's backstory.
The council left Shiala alone. I doubt they really care about Benezia's money or estates.
Liara is no spy, Liara is an information broker. She buys and sells info. Maybe she even made some bad business decisions in the beginning, we don't know this. I guess you can headcanon whatever you want here. I don't think she would have any contacts herself either. Benezia was probably one of the most powerful/influential asari in the galaxy, so Benezia connections would be my guess. But as mentioned above, remember that when we meet her she is a big fish in a small pond compared to the Shadow Broker or TIM who are big fish in the Ocean that makes up ME's universe. Two years should be more than enough for that, considering all circumstances (SB data, benezia's money, member of Shepards team). And this is a lot more believable than Tali's or Jack's new jobs, at least in my opinion. I agree that Bioware could have given us more info on how Liara started her business. But even Wrex became king of the krogan without a detailed explanation.
I never saw Liara as naive in general. She gets nervous around Shepard. But look at how she speaks with other characters like Ashley, Kaidan, Wrex or Allestia Iallis, she was definitely not "naive" or "meek".