Can independents run in open-list PR?

Short answer: it depends entirely on rules about ballot access.

Here is what I said when the question first came up two years ago:

Does this system exclude independents?

Not necessarily. Independents might run as individuals and win seats in their own right. They’d just need to clear the bar for a seat under proportional representation (roughly the number of votes cast divided by the number of seats in the district). Or they might form a joint “independent” list, which my colleague Mike Latner has seen under STV in Australia.

And the following should not be read to mean that one must be on a list to run. Again, this depends entirely on ballot access.

Who makes the lists? Rules vary. Party leaders might draw them up in a “smoke-filled room.” Local party committees might send delegates to a nominating convention. Multiple parties might negotiate a “joint” list. A single party might even field multiple lists. The point is that these lists exist in advance of a general election.

Magnus Jonsson also provides this resource, which has discussions of independents in Australia and Belgium.