In my two worlds (22 combined seasons), we don't have concrete rules on cash in trades, but here is what will happen for the following examples:
1 - Owner A has run out of cash just before the Amateur Draft and begs for mercy. Owner B shows pity and sends 500k to A for a non-prospect catcher who can call pitches.
The trade will go through, although "A" will take some flack in the forum for poor budgeting.
2 - New Owner A has taken over a rebuilding team with 6 top prospects and, shortly after budgeting is complete, posts that he will trade any and all prospects for $5mil each. Owner B immediately agrees to buy the best prospect for $5mil.
The trade will be vetoed. Well over a dozen veteran owners will believe that selling all prospects will make the team worse (no matter how the proceeds are used), won't trust "A" to stick around long enough to repair the damage in future seasons, and don't like the odds of getting a good owner to take over an even weaker franchise. This deal definitely hurts the world in more than one way.
3 - Owner A fleeces inexperienced Owner B in a trade (talent-wise) and also gets "B" to throw in $2mil in cash.
Vetoed. Even without the cash, several owners would probably veto and post about "predatory" practices, but having the money go "in the wrong direction" guarantees the veto.
4 - Mid-season, Owner A trades a good $6mil player (with team option for next year) plus $4.5mil to Owner B, who needs cash, for a good prospect. The values of the players (current for vet, projected for prospect) are about equal and the pro-rated salary remaining for the veteran is $3mil.
This one probably gets approved, but could be jeopardized if an Owner X vetoes early, messes up the math, and posts that $10.5mil (or $7.5mil) is going in one direction. If that happens, then someone else (most likely A/B) must respond quickly that the net is really $1.5mil, which would be the cost of next year's option buyout.
I will grant that the vetoes in #2 and #3 are made easier by having new/inexperienced owners involved, but cash-for-prospects is a hot button and would be unpopular even with a long-time owner. In #3, if Owner B had been around for 10 seasons and had had some success, the deal might slip through with a "Manny being Manny" treatment.