Can I calculate ROW_NUMBER() for only consecutive records?

I was able to address this using LAG():

SELECT
    Sequence, Subset,
    CASE WHEN Sequence = 1 OR Subset <> LAG(Subset, 1) OVER (ORDER BY Sequence)
        THEN 'New subset'
        ELSE 'Continuation'
        END
FROM
    @Data

This returns "New subset" for records #1, #4, and #6. Apparently LAG() partitions slightly differently from ROW_NUMBER().

Obviously this doesn't provide row numbers, but it helped me reach the goal of identifying consecutive sequences of numbers, when the subset identifier can repeat.

What we do here is,

1. Calculate resets (column rst in code)
2. sum() to get groups (column grp in code)
3. Get the row_number() from the grouping.

Code,

SELECT row_number() OVER (PARTITION BY grp ORDER BY sequence) AS number,
  sequence,
  subset
FROM (
  SELECT count(rst) OVER (ORDER BY sequence) AS grp, *
  FROM (
    SELECT CASE WHEN subset != lag(subset) OVER (ORDER BY sequence) THEN 1 END AS rst, *
    FROM foo
  ) AS t1
) AS t2;

You can see the DBFiddle with results here

• https://dbfiddle.uk/?rdbms=sqlserver_2017&fiddle=13de970857770ce27462565b4063e1d0