I can only answer from a US perspective, i.e. not sure how things are mandated in other countries.
The answer is contained within the publicly accessible Robinson maintenance information, which also references the relevant Lycoming maintenance information.
https://robinsonheli.com/r44-maint-manual/
Above 2200 hours:
The answer is simple--throw away the life limited components and do the airframe overhaul. Same for the engine.
Hit the 12 year mark with less than 2200 hours and the answer becomes more complex because there are options:
If you look at Chapter 3, per the FAA type certificate you will see that the only parts that are CALENDAR limited are the main and tail rotor blades. Thus, if you have reached a 12 year calendar anniversary on an R44 but have not gone 2200 hours operating the remaining life limited components on the list, per the FAA the remaining components may remain in service if found in airworthy condition.
Where it gets a little subtle is that while Robinson recommends a 12 year inspection on those remaining components the FAA does not mandate it. So you can legally continue to run the helicopter in the US past the 12 year mark without doing a Robinson recommended and described (Chapter 2, Section 2.600) 12 year inspection. If you do decide to do a 12 year inspection (not overhaul, i.e. you are not throwing away the life limited components listed on the type certificate early) it should cost you around $40K USD. People do it both ways all the time.
Where the engine is concerned you have to follow Lycoming's instructions, which, as called out in the Robinson service manual, is Service Instruction (SI) 1009. That SI says that at 12 years the engine must be overhauled unless:
"For FAA Part 91 or EASA Part NCO (non-commercial) operations, only an appropriated rated and qualified maintenance person (or international equivalent) can allow the twelve (12) calendar year TBO to be exceeded after thoroughly examining the engine for corrosion and degradation in accordance with 14 CFR 43 Appendix D (or international equivalent) and determining that the engine remains in an airworthy condition. This inspection is to be repeated annually or as necessary to ensure continued airworthiness."
So under the right conditions you can allow the engine to go on-condition until 2200, although it may be that you start replacing seals and whatnot, and if the compression is starting to drop any A&P is going to tell you to throw in the towel and overhaul it.