Beggarware is a slang term for free software that depends on donations to fund further development. The creator or creators of beggarware release a free and functional version, and then wait for voluntary donations to justify the effort needed to improve it. Beggarware is often used as a derogatory term to refer to freeware.
Techopedia explains Beggarware
Beggarware usually contains an appeal for a donation from users who find the software valuable. The success of this approach in funding development is not known. Some users of freeware are no doubt opposed to paying for any software, whether by donation or purchase, but presumably enough people donate to justify the wide range of beggarware available.
The beggarware approach of soliciting donations rather than charging upfront has spread to website templates, image galleries, desktop wallpaper and other areas beyond software.