Yes, this is true. The original signature will no longer be valid.
Ideally the mailing list itself will add its own signature, and the receiver will use the mailing list signature when determining the disposition of the message.
>is there anyway to deal with this issue so that our users are able to receive the message?That depends on why your users are unable to receive the message? Are you preventing delivery on messages that are missing a DKIM signature? As you can see, that is probably not a good idea. At the least, it should only be done for messages claiming to be from a domain that always signs its mail and never sends mail through a mailing list that alters messages.