I believe King Umberto II had enough family wealth to support him and his family during his exile in Portugal.

First he took residence in Villa d'Este in Cascais, a villa belonging to the wealthy Pinto Basto family, linked, among others, to the prestigious Vista Alegre group, Portugal's most porcelain factory. He lived there from 1950 till 1961.
Then, a group of italian monarchics gathered and contributed to the building of another house facing the Atlantic Ocean, next to to Villa d'Este.
The King himself choose to name it Villa Italia.
The King led a lavish life in Cascais and gave memorable and faustuous parties, to which attended his neighbour exilès, the Bourbons/Barcelona, the Orléans and even the Braganças, then living near Coimbra in the middle of Portugal.
His sumptuous lifestyle allows to infer a generous bank account.

The King supported several charity institutions in Portugal and his house was always opened to the italians who wished to meet him.

https://www.granderealvillaitalia.realhotelsgroup.com/pt-pt/historia-do-rei-humberto-ii/
http://royal-splendor.blogspot.com/2022/03/villa-italia-king-umberto-iis-home-in.html
https://www.tripadvisor.pt/LocationPhotoDirectLink-g189154-d634774-i222522666-Grande_Real_Villa_Italia_Hotel_Spa-

After the King's death, his heirs sold the house to a hotel group, who built a large 5 star hotel on the grounds of Villa Italia and Villa d'Este, the Grande Real Villa Itália Hotel & SPA

https://www.tripadvisor.pt/LocationPhotoDirectLink-g189154-d634774-i222522666-Grande_Real_Villa_Italia_Hotel_Spa-Cascais_Lisbon_District_Central_Portug.html
https://www.casamentos.pt/hotel-casamento/grande-real-villa-italia-hotel-&-spa--e51073

On top right photo, you can appreciate Villa Italia's priviledged situation, facing the ocean.