Do we need to subscribe to any special plans to receive such service? Or do they do that regardless of warranty and when/where the product was bought?

I bought the on site service warranty. It was about 100 Euro for 3 years (as in 33.33 per year) for my zBook 15 back in 2014. It got much more expensive on the fourth year (maybe 100+ per one year), then basically started to cover nothing. I got a quotation for 400 Euro to replace the keyboard. The original backlit one is about 130 Euro, the not backlit one is about 40. Of course the difference is next business day replacement but for a keyboard it's never so vital. I already replaced it myself a couple of times and bought a spare one because they'll run out of parts sooner or later. I keep my old laptop as a spare and kind of know what to buy next, ideally the same laptop, maybe a little lighter and with no number pad.