A quick definition of personal suretyship:

Personal Suretyship: When someone promises to pay back a debt or fix a problem if someone else can't do it. This is called being a "surety." The surety and the person who owes the debt are both responsible for paying it back. Sometimes, people become sureties to help someone who doesn't have enough money or credit. There are different types of suretyship, but personal suretyship means the surety is responsible for paying damages if something goes wrong.