Her baptismal index:

First name(s) Penelope
Last name Cartwright
Gender Female
Baptism year 1770
Baptism date 23 Feb 1770
Place Wellington
County Shropshire
Country England
Father's first name(s) Thos
Father's last name Cartwright
Mother's first name(s) Penelope
Record set England Births & Baptisms 1538-1975

from FindMyPast ex familySearch.
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No clear children found in the Shropshire / Radnorshire region, though several William Wilson Archibald births, marriages and deaths were found.

I wonder if this burial might have been hers:

First name(s) Penelope
Last name Archibald
Gender Female
Marital status -
Occupation -
Event year 1823
Birth year 1771
Age at death 52y
Death place St. James, Manchester, Lancaster, England
Burial year 1823
Burial date 13 Mar 1823
Burial place -
Place Manchester
County Lancashire
Country England
Record set England Deaths & Burials 1538-1991
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Their marriage transcription:

First name(s) Penelope
Last name Cartwright
Marriage year 1792
Marriage date 26 Sep 1792
Marriage place Wentnor
Denomination Anglican
Residence Wentnor
Spouse's first name(s) William
Spouse's last name Willson
Spouse's residence Raydar, Radnorshire
County Shropshire
Register date range 1754-1812
Archive reference P296/A/3/1
Page 37
Register type Marriage & Banns
Record set Shropshire marriages
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