A Direct answer: a loan that is based on financial need is typically called a need-based loan. Further context and common examples:

• In education finance, need-based aid or loans are awarded based on the borrower’s demonstrated financial need, often determined by family income and assets. Examples include Direct Subsidized Loans for undergraduate students in the U.S., as well as various need-based grants and work-study programs offered by federal, state, or institutional programs.

• In housing and consumer lending, some programs are targeted to borrowers with low or moderate income, where approval and terms consider income as part of assessing need; these are often described as need-based or special programs designed to assist lower-income applicants.

If you’d like, I can tailor this to a specific type of loan (educational, mortgage, personal) and explain how need is determined and what documentation is typically required.