I'll answer that one.
Just applying for welfare is not enough to search without probable cause. The government should absolutely not be allowed to search your personal property for that.
Perhaps you should read what the spirit of the law was that Fourth Amendment was written to address: Writ of assistance - Wikipedia, the free encyclopedia
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.