There is no point to sending a message body with a 304 response. From RFC 9110:
The 304 (Not Modified) status code indicates that a conditional GET or HEAD request has been received and would have resulted in a 200 (OK) response if it were not for the fact that the condition evaluated to false. In other words, there is no need for the server to transfer a representation of the target resource because the request indicates that the client, which made the request conditional, already has a valid representation; the server is therefore redirecting the client to make use of that stored representation as if it were the content of a 200 (OK) response.
(Below is the original content of this answer based on the earlier RFC 2616:)
In fact, the HTTP specification says that the server must not do so. If you have one that is, it's misbehaving according to the spec.
From the HTTP Specification:
The 304 response MUST NOT contain a message-body, and thus is always terminated by the first empty line after the header fields.