One of the problems in porting mail from Qualcomm's excellent, but unfortunately no longer supported, Eudora e-mail client to other email clients (such as the open-source Mozilla Thunderbird, which is, incidentally, Eudora's legitimate successor) is that Eudora (quite idiosyncratically) does not encode attachments into email messages, but rather keeps them in separate locations, dispersed through your system.
Some Eudora importers, such as the one bundled with Mozilla Thunderbird, are able to identify attachments linked to received messages, locate said attachments in your system, and encode them into the imported messages, thus storing everything in a single database. These utilities, however, are generally beset by the problem that they do not do the same thing for sent messages. In other words, although there are Eudora importers out there that are able to succesfully import received attachments, I do not know of any utility that, provided as-is, does the same for sent attachments.
The following little Java program attempts to solve this issue, by preparing your Eudora mailbox files to be more seamlessly importable by Thunderbird. What the program does is it extracts the path associated with each sent attachment (stored originally in the "X-Attachments" header field), and copies it to the bottom of the respective message after the words "Attachment Converted." Ultimately, this new field allows Thunderbird's Eudora importer to "realize" that sent attachments actually exist, which in turn allows it to look for and effectively import those attachments.
Be warned that any importer will only effectively be able to import the files that it can find. In practice, this means that if there is any discrepancy between the paths stored in your messages and the actual location of those files, no importer would be able to do its job for that file. Please also note that no importer is capable of bringing deleted attachments back into existence! If they're gone, they're gone (sorry!). Also, please be advised that this program was designed for and originally tested with Thunderbird's Eudora importer. It might well work with other email clients' Eudora importers, but I have not personally tested them. If you do test them, please let me know the results.
Downloading this tool is free (donations accepted!), but be warned that it comes with absolutely no warranty and, therefore, you should use it at your own risk. The program is distributed under the GNU General Public License, so feel free to modify the code as you need to. Otherwise, you may simply choose to download the ready-to-use binaries.
As of now, the tool is (unfortunately) only compatible with the Windows version of Eudora. To read more about Mac compatibility and how you can help make this utility more Mac-friendly, click here.
Lastly, be sure to read the readme before you use the utility. Good luck!
Download: