Picture a net stretched under a whole country. Most of the time nobody thinks about it. Then someone loses a job, or falls ill, or gets too old to work, and the net is what stops the fall — money while they look for work, a doctor they can afford, a pension. The net is paid for by everyone's tax, so it belongs to everyone and everyone argues about it. Once you can see the net, the second use follows on its own: a country can be named after the net it has.
The source records the phrase as a compound of welfare + state, which lines up with the picture: a state whose job includes keeping people well.
資料來源把它記成 welfare 加 state 的合成詞。字面就是「照顧人民過得好的國家」，正好對上那張網的畫面。
Wiktionary entry supplied in this packet (etymology_text: 'Compound of welfare + state.')
One branch
那張網，以及底下有那張網的國家
兩個意思是同一張網的兩種看法：一種看的是網本身，一種看的是網底下的那塊地方。文法會告訴你是哪一種。
noun · C1
The whole system a government uses to look after people who cannot support themselves at the moment: money for people out of work, free or cheap medical care, and help for people who are ill, old, or raising children.
社會福利制度