One alternative to creating a partial buyout - which is what an equity redistribution would amount to - is to have the additional cash treated as a loan.
The advantage is that this lessens the likelihood of hard negotiations between the founders and the potential for hard feelings which is a risk in those situations. I.e. it avoids the distraction of arguing over shares in what is probably a dead man walking.
The interests of both parties are in keeping the company going. When one or more cofounders give a priority to getting more equity, things are less likely to end well and more likely to end sooner.
Supposing that in your scenario, one founder puts in $10,000 and gets 10% of the other founder's stock. Assuming two founders and a fifty-fifty split, that means the company is now valued at $100,000 and the selling founder (that's the one without cash) has realized capital gains of $4950 upon which he will owe taxes.
He may also be pissed off because the real equity, his sweat doesn't fall into the equation. Maybe 45-55 isn't so bad. But each time this happens, the broke founder has less potential upside. And he's been forced to sell. And to sell cheap.
As his equity is reduced, his incentive to walk away is greater. In other words, reducing his equity reduces the alignment between his interests and that of the other founder.
Conversely, if the loan is unlikely to be repaid, then the additional equity probably isn't worth anything anyway.
An advantage of a loan over partial buyout becomes more apparent if the company is liquidated - let's suppose for $4000. In the partial buyout, the 55% stakeholder would receive $2200 and the other stakeholder $1800. In the loan scenario, the lending party would recover $4000 and the other founder nothing.
Would this make it fairer in all situations?
First it prioritizes cash over effort. This expresses a lack of faith in the startup. Second nothing poisons personal relationships like debt. Third it means that B has an incentive to quit and get a regular job earlier in the company's life cycle because he has an additional bill to pay.
Arm's length marriage is not a good idea.
I think the personal loan makes a hash of things. Suppose founder B writes the critical piece of code? Should he require founder A to pay for it? Suppose he makes the critical sale, should he get more equity?
Founders bring different resources to the enterprise. If one founder is unable to contribute a critical resource, the sensible options are to find a working source or forgo the enterprise.
If you must have your money back, don't invest in a startup.