FWI the liturgical anointing of the sick is also a part of the liturgy in many Lutheran and Anglican/Episcopal parishes.
While is it sometimes offered as part of the Sunday liturgy it is more commonly offered during midweek liturgies; generally at the same time as the Communion distribution.
I’m sure if someone is suffering from cancer, going in for surgery, etc. that it is also given individually. That’s the norm in the Catholic Church — although it is offered at special healing Masses. (As far as I know — but perhaps I am mistaken.)