It is impossible to give a good and specific answer to this question without knowing the details of “the welfare program.” Different countries have different systems of welfare and so this answer differs from country to country and even to some degree from state to state in the US. It is also very hard to objectively answer this question as economists differ on the impact of welfare programs.
It is possible to argue that welfare programs are good for the family and the economy. They help keep families out of poverty. They help to ensure that even poor children have adequate food and medical care. They ease the stresses that poverty puts on families. They help the economy by giving these poor people some spending power and by helping to ensure that poorer children become educated and can hopefully contribute to the economy when they are older.
However, it is also possible to argue that such programs are bad for the family and the economy. They are said to hurt families by encouraging dependence on the government. They create a system where poor people do not have enough of an incentive to work. By doing this, they harm the family, but they also harm the economy. They allow people to get by without having to become productive members of society who help its economy grow.
Thus, it is possible to look at welfare programs in general in either of these ways.