Can you provide an example including the desired result? Do you mean when the left frame is null, or when the right frame does not have a matching row but does have a null value?

Does this example clarify the desired result?

import polars as pl
from datetime import datetime

df_expected = pl.DataFrame(
    data=[
        (None, datetime(2024, 1, 1, 0, 0, 0), 5),
        ("a", datetime(2024, 1, 1, 0, 0, 0), 5),
    ],
    schema={"category": pl.Utf8, "timestamp": pl.Datetime, "value": pl.Int8},
    orient="row",
)

df_left = df_expected.drop("value")

df_right = pl.DataFrame(
    data=[
        (None, datetime(2023, 1, 1, 0, 0, 0), 5),
        ("a", datetime(2023, 1, 1, 0, 0, 0), 5),
    ],
    schema={"category": pl.Utf8, "timestamp": pl.Datetime, "value": pl.Int8},
    orient="row",
)

df_actual = df_left.join_asof(
    other=df_right,
    on="timestamp",
    by=["category"],
    strategy="backward",  # join_nulls=True
)

I see--I believe you're asking that the initial by=... include the ability to join on nulls.

I think there is an issue which is that joining on nulls produces the cartesian product of the matching records, and these are not guaranteed to have a sorted output order, which is a requirement of join_asof. But of course if the join itself is producing those records, it could probably sort them.

I think there is an issue which is that joining on nulls produces the cartesian product of the matching records,

Isn't this also true for any other values? What is special about nulls here (in the by part, not the on part)?