Some foreign nationals are allowed to work under specific circumstances due to a labor shortage. This might well cover the scenario you gave.

Japan has the Immigration Control and Refugee Recognition Act, which is a Japanese law that governs the entry, stay, and departure of all individuals, including those seeking refugee status. It aims to establish equitable control over immigration and streamline the process for recognizing refugees.

People cannot apply for asylum without reasonable grounds

If someone overstays a visa, works illegally, etc. there is a specific process to follow. If they are going to be deported there is typically a detention beforehand. Once deported they cannot reenter for 5 years

Individuals with compelling reasons for overstaying, such as medical emergencies, may be granted special permission to stay.

Individuals who voluntarily surrender to immigration authorities may qualify for a reduced re-entry ban.

Japan has revised its law to allow individuals to apply for special permission for residence during the deportation process.

Guidelines for granting special permission consider factors such as familial ties, marriage to Japanese nationals, and whether the individual is stateless.

In December 2023, the government introduced a measure to grant special visas to children born and raised in Japan to undocumented foreign parents.

As for vagrancy, Japan's approach to homelessness is complex, with a focus on supporting individuals' return to self-sufficiency through employment and housing assistance. This might also cover the scenario you gave