Italian living in Germany working for Italian company, is it possible?

How can you live here without residing here? I thought the two words mean the same.
Or, since "residence" can also mean place to live, are you homeless?

In any case, it is of course possible to work for a foreign company whileliving in Germany. We hav discussed this several times on this forum - please search for related threads and read them!
In short: Because the company cannot fulfill the obligations of a German employer (like deducting taxes at source and paying for social security), you will be classed as self-employed. That involves a layer of complexity and cost, which you should thoroughly understand before embarking on this. You also need very good German language to deal with the buerocratic aspects (business registration, taxation, accountancy) - or engage professional consultants for them (at a fee).

As an Italian citizen you can work in Germany. Doesn't matter where the employer is located. But you will have to register and also report all of your world-wide earnings in Germany, pay tax and social contributions and your health care premiums.

Normally, a German employer has to pay half of your heath care. Since your employer will be in a foreign country, you will likely have to pay 100%, as if you were self-employed.

In the end you should not get taxed in Italy as well but working out the details to make sure this doesn't happens might be complex. Possibly the employer can clarify this with the local authorities if needed...