The issue is one of trust.
The CEO/Directors can give you access to the corp. hangars (for items) and corp wallets (for ISK), if they trust you. Once you have access, you can take everything out of there and put it into your personal hangar / wallet. Nobody (but you) has access to take stuff back out of your personal hangar and personal wallet.
Because of this game mechanic, it’s very unlikely that the CEO/Directors will trust you with the corp or alliance wallet. By necessity, some funds are set aside to pay office rental and other fees, and some of the veterans who have been in the corp for a long time may be trusted with access to these funds, but there’s no guarantee that they won’t take stuff and run.
But don’t let that discourage you. You can certainly ask to trade for the corp, and see what they say. They’ll likely give you access to a smaller sum, to start with, and possibly increase it if their trust grows. As the others have said, though, it’s easier to build a relationship with the rest of the corp by participating in activities (PVP or PVE) that the corp organizes for everyone, than it is to ask for access to money from the start, and then build trust by not stealing.
EDIT: Corps don’t recruit “traders,” and they don’t recruit “miners”, “remote repairers” (healers), etc. Any character can train anything, so unlike other MMO’s where they may be lacking healers or tanks or whatever, in this game it’s a simple matter to just add some skills to the queue and voila. It’s safer to just ask the existing members, hey guys can you train up some logistics ships for remote repair, than it is to recruit outsiders who have those ships unlocked. So as a result corps don’t look for roles, they just look for “active, trustworthy players, who have compatible personalities and like the same jokes / activities that they do.”