Co-signer
A co-signer is a person who signs a lease or loan alongside the main applicant and takes on the same legal duty to pay. If the tenant misses rent, the landlord can collect from the co-signer. Parents co-signing for students and young workers is the familiar case.
A co-signer is the most common fix for an applicant who does not make 3 times the rent. The landlord screens the co-signer instead, checking that person's income and credit, and often sets the bar higher than 3x because the co-signer has a home of their own to pay for.
People use "co-signer" and guarantor to mean the same thing, and many leases do too. Where a distinction is drawn, a co-signer is a party to the lease with the right to occupy, and a guarantor only backs the payment.