When the Church celebrates a sacrament, we pray for the encounter with Christ to be a fruitful one. Perhaps physical healing will not be the result of anointing. A communal celebration of those being anointed and those praying for the sick will be an expression of Christian mercy, of trust and hope in a loving God.
If you know of a person who would benefit from the sacrament—someone who has recently fallen ill, or an older person who is weakened without any new illness—contact the staff at the parish, or make arrangements to bring them to Mass June 25th or 26th.