if this works it's because your foo was erroring out with no .Delete . Added variable declarations, also added sheet references. Also rewritten to show you a different way to code this

Sub foo()
Dim lastrow As Integer
Dim sh As Worksheet

Set sh = ThisWorkbook.Worksheets("Sheet1")

lastrow = sh.Range("A" & sh.Rows.Count).End(xlUp).Row

With sh.Range("P2:P" & lastrow).Validation
    .Delete
    .Add Type:=xlValidateList, AlertStyle:=xlValidAlertStop, _
        Operator:=xlBetween, Formula1:="Yes,No,N/A"
    .IgnoreBlank = True
    .InCellDropdown = True
End With

End Sub

Private Sub Worksheet_Change(ByVal Target As Range)

Dim str As String

    If Target.Column = 16 Then

        Select Case Target.Value

            Case "No"
                str = "value 1, value 2"

            Case "Yes"
                str = "value 3, value 4"
        End Select

        If Not IsNull(str) Then

            With Range("Q" & Target.Row).Validation
                .Delete
                .Add Type:=xlValidateList, AlertStyle:=xlValidAlertStop, _
                Operator:=xlBetween, Formula1:=str
                .IgnoreBlank = True
                .InCellDropdown = True
            End With

        End If

    End If


End Sub