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During late Arrow Season 2, Isabel Rochev successfully contrived to become CEO of Queen Consolidated, whereupon she began breaking up the company and selling it off. By having the board issue further stocks, and taking out loans by using stocks and company property as collateral, Isabel diluted the worth of the stocks owned by the Queen family (and by that point, the Queens, the Starling National Bank, and Stellmoor International were the only stockholders left in Queen Consolidated). She also repossessed Verdant, the nightclub which Team Arrow used as a cover for their headquarters.
...however, Isabel could not have touched Oliver Queen's trust fund, or Thea's, or the actual stocks owned by Oliver and / or Thea (she just devalued the latter) - and Isabel did not have very much time in which to sell off company assets prior to her death.
It's also possible that Isabel had not yet finished hammering out the legal agreements surrounding some or even most of the loans she took out using QC stocks and property as collateral. A process like that generally takes weeks at minimum, sometimes months - and Isabel only held the post of CEO at QC for, what, two or three weeks at the most? So how much of this process did she actually complete, prior to first her official 'disappearance' (after Diggle shot her, and Deathstroke subsequently revived her with Mirakuru) and then her death at Nyssa Raatko / the Warith al Ghul's hands? Theoretically speaking, it might even be that the various companies' and banks' legal departments had not yet finalised anything on any of those loans.
Then there's the matter of Isabel selling off parts of QC. Again, asset stripping a large multinational Fortune 500 company (even a fictional one) is a lengthy process: no sane person throws around sums of tens of millions of dollars without taking a lot of precautions first to make certain they're buying exactly what they expect to be buying, and that takes weeks or months, or even years. And if Isabel were only the CEO of QC for less than a month, maybe only two weeks or so? Then I seriously wonder how much of QC she could have successfully sold in such a short time - or if she had time to finalise the sale of anything at all?
The bottom line is that as of Arrow 2x23's final scene, Oliver would be 'cash poor' - and if his trust fund only had a quarterly payout, then he would need to wait until 1st of July before the next one. But the bones of QC would still exist at a bare minimum, and Oliver would be the majority stockholder; and after the probate on Moira's will was executed, Oliver would likely own his family's mansion free and clear. (Unless Moira bequeathed it to Thea or Walter, or someone else entirely.)
Then there is the matter of Stellmoor International: Isabel's criminal actions prior to her death should have been publicly exposed, and thus resulted in a tidal wave of negative publicity for Stellmoor. Put bluntly, Stellmoor should have crashed and burned and filed for bankruptcy because of that disastrous situation - thus enabling Oliver to buy up the remaining stock in QC for a fraction of what Stellmoor originally paid, after Stellmoor's assets came up for sale. Repaying the loans which Isabel took out might have been relatively complex, but so long as they were repaid quickly enough, then no interest payments would need to be made, thus saving quite a lot of money in the long run. (Assuming, of course, that the paperwork surrounding said loans had been fully thrashed out by that point: if it were still a work-in-progress, then it wouldn't be a problem at all.)
Put another way? If what happened with Queen Consolidated and Oliver's finances had played out logically after Arrow Season 2 ended? Then Oliver should have had less liquid assets, but he would have become the majority stockholder in QC, with the Starling National Bank owning the remaining 5%. (The latter situation being the result of events from Arrow 2x01, when Walter helped Oliver to get one over on Isabel.) It is also possible that Oliver could potentially have bought up the bank's stock in QC at some point in the future - which would have made Oliver the only stockholder (and thus the sole owner) of QC. Oliver could easily have stayed on as CEO, or asked Walter to return to the position so Oliver could become 'the power behind the throne' and only show up to routine meetings of the board of stockholders - and if Oliver became the sole stockholder, then it would just have been him and Walter going over the company's performance in the latest quarter.
...all of which means that what happened in Arrow 3x01 to enable Ray Palmer to steal ownership of QC was completely illogical, irrespective of Ray's hacking QC's servers to steal data to prove his points during his presentation. That entire plot arc was the result of Bad Writing and Planning from the show's production team.
As for funding Team Arrow? Well, Deathstroke and his minions were burning some serious money on their illicit operations - so they had to have substantial amounts of less-than-legal financial resources at their disposal. It is entirely plausible that Felicity Smoak / Overwatch could have tracked down at least some of these funds and 'appropriated' or 'confiscated' them for Team Arrow to put to better use - and perhaps anonymously donated a generous percentage to various charities in the process, using the remainder to finance Team Arrow. (After all, trick arrows don't grow on trees.)
Again, the fact that this did not happen on the show during Season 3 was the result of Bad Writing and Planning.
So, if you are thinking of writing an AU Arrow fanfic set after the show's second season, and you want to handle the ownership and running of Queen Consolidated in a much more logical fashion than the show did during Season 3? Please bear these points in mind, and see if they give you any ideas.