I think something, that European countries including Italy are rapidly needing a Young population, that they should give more opportunities to people from other countries to be able to settle , only those immigrants who do contribute to a country and that they are given facilities to have a Family and make a life there, I think that would help a lot, but Italy's problem is escalating very quickly to worse.
There is a process in order to become a legal resident in Italy, in Europe, and in any other country of the world. Proposing to let people in from other countries just because there is a demographic downtrend makes little sense. If you want to move to another country you must bring something with you: money, skills, etc. Letting poor people in is just going to create more and more problems because many illegal immigrants just ask for money and shelter, they have no intention of working, no intention of integrate, no intention of paying taxes, they just want to exploit the system. It doesn't work like that.
If you just open your borders because of a drop in population, the country might face bigger problems. There might increase in criminal activities since most of these illegal immigrants don't go through security checks. A handful of European countries are going through insecurity because they were liberal. But letting people who need protection shouldn't stop, even if they are poor.
But the problem with the Italian National team is not a lack of players. Italy produces some of the best players in the world. Immigrants could just be an addition and not the main source for national team players.