I'd like to ask the widowed elderly who have no room and a monthly pension of 4 thousand, can they apply for public rental housing?

You can apply for public rental housing. Public rental housing is aimed at low-income families with housing difficulties, including those who have passed the qualification examination of affordable housing and price-limited housing, as well as other families with housing difficulties, as well as newly graduated college students and migrant workers. Public rental housing is used by the government to solve the housing difficulties of newly employed workers and other groups. Legal basis: Article 7 of the Measures for the Administration of Public Rental Housing shall meet the following conditions: (1) There is no room in the local area or the housing area is lower than the prescribed standard; (two) the income and property are lower than the prescribed standards; (3) If the applicant is a migrant worker, he has been employed stably in the local area for a specified number of years. The specific conditions shall be determined by the housing security department of the municipality directly under the central government and the people's governments at the city and county levels according to the actual situation in the region, and shall be implemented and announced to the public after being approved by the people's governments at the corresponding levels.