First, INEOS can absolutely afford to buy the club. Their annual income last year was something like $17billion, with a similar amount held in assets. Their wealth dwarves anything required in this deal.
But it's normal practice for even extremely wealthy businesses to finance purchases they could nonetheless buy outright, because factors like liquidity carry more value to them than the cost of borrowing and allow for further reductions elsewhere (e.g. in how they are taxed). It's important to understand that the concept of debt you have from your everyday life (like getting a loan to buy something you couldn't otherwise afford) isn't its only function.
Understanding that, would money need to be taken from Manchester United to fund the repayments INEOS have to make? No. Because again, their annual earnings are so vast that any money they could take from United is a relative pittance. Always keep in mind, the total cost on us of the Glazer's entire time here is a fraction of what INEOS make in a year. United doesn't have to pay for its own purchase in this scenario any more than any other asset INEOS buy does.
Whether they would actively put money into United is a different question, but in truth we wouldn't particularly need them to. If the debt is cleared, stadium rebuild financed and the club keeps what it earns then we are wealthy enough to be competitive without additional investment beyond that.