Are they allowed to take out loans without paying them back? If they have to pay them back, eventually they have to use that collateral which will be a taxable event. They might be able to delay, but they'll eventually have to pay.

"Buy, Borrow, Die" is the talking point. Cost basis of the assets gets stepped up at death so the inheritor can pay off the loans at that point in time without paying taxes on capital gains.

Then this seems to be the loophole that needs to be resolved. Before the estate pays out, the debts should be settled within the estate using the cost basis belong to the deceased. Assets paid out after loans are satisfied should then have their cost basis reset (if that happens at all, I don't want to take a stance either way if that should happen, except it should only apply once loans are repaid if it ever does apply).

Mechanically, I don't think that works. What prevents the debt from attaching to the inheritor before death (e.g., co-signed loan)? The only solution here is eliminating the cost basis step-up at death.

Could they not make sure that enough of their assets are in cash-flowing assets (think, rent-yielding assets, or treasuries, or dividend-yielding stock, etc.) that need not be sold and whose cash-flow can be utilized?

All those cash flows are taxed.

They invest the loans and make even more money. No need to sell anything ever.