Here's one UK based scenario.
An aircraft takes off from private land into Class G airspace. No flight plan required, no R/T call to be made.
The aircraft continues under IFR and IMC, remaining in class G towards its destination airfield. At some point near the airfield it will enter controlled airspace. The pilot calls the appropriate ATC unit in advance, obtains an IFR clearance to enter the airspace and is given direct routing to the approach.
What ATC service, if any, the pilot obtains en route is up to the individual.
All perfectly legal, although it might not always work in practice. Other things like destination PPR and obtaining a slot might be needed.