In a technical sense, no, you cannot ‘inherit' debt. There are, however, some common ways an individual's death or business dissolution can result in the burden of debt shifting to another individual, entity, or even to another trust.
Upon a person's death, their estate undergoes a process called ‘probate' or a comparable settlement process. Whether the deceased had a valid will or trust directing the distribution of their assets or whether they left the distribution to be done by default under the law, every estate must first be settled before any distribution can occur. Settlement includes identification and collection of the deceased's assets, including cash, property, insurance payouts, and other things of value, and identification and payment of the deceased's debts.
Upon settlement of a deceased person's estate, the distribution of assets can only occur if assets still exist—i.e., if the assets are more than the deceased's debts. A would-be beneficiary of all or part of a loved one's estate might find that their expected inheritance is substantially less than they expected or possibly even reduced to zero because their loved one had a comparable amount of assets and debt at the time of their passing. In that sense, it may feel to the beneficiary as though they ‘inherited' debt, especially if the balance of the assets is reduced to zero and the beneficiary is then strapped with paying out of pocket for any death-related expenses, including funeral costs. In a strict sense, however, a beneficiary does not become the owner of a deceased person's debt simply by virtue of being a default or even a named beneficiary.
In cases where one individual has co-signed for, say, a car loan and the principal borrower passes away before the loan is fully repaid, the co-signer could ‘inherit' the debt remaining on the loan. During the estate settlement process, the deceased borrower's assets should first be used to pay such debts, including liquidation of assets such as the car itself, and the co-signer should not be on the hook for the loan as long as the assets cover all of the deceased's debts. Where the deceased's assets are insufficient to cover their outstanding debts, the remaining debt will be shifted to any and all co-signers. It should be noted that this type of debt ‘inheritance' only occurs because the co-signer took the knowing and intentional action of offering up their own assets in the event of non-payment. A person who does not voluntarily or legally attached themself to a debt, whether conditionally or otherwise, cannot be held liable for it.
Upon the dissolution of a business entity, debt may be transferred to an individual. When a corporation dissolves, for example, the Articles of Dissolution or comparable filing must indicate whether there are assets or debts and which taxpayer(s) assume any or all of either assets or debts. More commonly, a business will close, such as a restaurant, where one or more individual founders or owners put up there own credit or collateral to secure a line of credit for goods or services necessary to the operation of a (typically new) business. For such non-corporate businesses, any individual or other business entity that guaranteed the debt at issue upon business dissolution will, in sense, ‘inherit' that debt. As with cases of personal guarantees, like the car loan example above, the ‘inheritance' of business debt should not surprise the guarantor or business partner because the potential liability for business debt should be understood and is assumed to be understood when an individual signs a legally binding document accepting such liability.