But shelter operators and advocates for the poor said the move did little to ease the pressures that shelters are facing.
The city expects that there will be few such cases, Ms. Nussbaum added, and the shelter operators agree.
"You can get a good sense of increase when shelter operators say, 'We served this many more people a year.' "
While most shelter operators say the counseling work is no different from what they have done in the past, they now have a monetary incentive.
But other shelter operators say immediate veterinary care doesn't always make fiscal sense.
She said the city would sever ties with the shelter operators who evicted the men, women and children.
The city contracts with private shelter operators to provide services for the homeless.
Neither the shelter operators nor city officials have estimated how many homeless families might be evicted because they do not meet welfare eligibility standards.
The intake center and shelter operators will also share information about abuse, a practice not now followed.
The new rules, shelter operators and homeless advocates said, can be draconian.