In the U.S., it is not the act of attempted suicide that creates eligibility for Social Security Disability Insurance (SSDI) payments but the underlying mental illness. There's also Supplemental Security Income (SSI) payments which some people also refer to as 'disability'.
Both are administered by the Social Security Administration. SSDI eligibility typically requires having paid Social Security taxes; SSI does not have that requirement, it is needs based.
Yes, literally anybody can apply.
This link explains some of the specific requirements for both SSDI and SSI:
https://www.ssa.gov/planners/disability/
While anybody can apply, I can tell you that I know from personal experience that if you don't have an experienced doctor who knows how to work within the confines of the Social Security system and/or a long documented history of mental illness, it can be a long process to get approved nowadays. Apparently there is a back log of applications so they just outright reject some initial applicants, who eventually get approved on appeal, which can take a couple years.