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When it comes to getting rid of old client files of the paper variety (after at least five years, of course), there's really only a couple good options: burning or shredding. The latter is much more environmentally friendly, as shredded paper can be recycled, whereas burnt paper just releases chemicals into the atmosphere needlessly.
However, for old digital files, neither burning nor shredding will really get rid of them (okay, maybe burning might, but it might not and you'll never really be sure, and it's probably not worth the risk, dangers, and bad smells, of burning electronic equipment). And just taking a hammer to a hard-drive won't prevent dumpster diving tech thieves from trying to reconstruct digital files on destroyed drives.
When to Get Rid of Digital Files
For digital files, you should maintain the same destruction schedule as paper files. So when you finally get around to destroying a box of paper files, you should cleanse your computer systems too. While you may think that digital storage is cheap, and thus you should keep everything, you're really just making it harder on yourself. If there are certain pleadings you want to keep as samples, or mementos, that's fine, but don't hold onto entire digital case files because you're too lazy to scroll through the files and see what's there.
Eventually, your digital storage will fill up, and, even if it doesn't, you're putting needless strain on your computer systems, and requiring more data to be backed up than necessary (because you do have an automated backup system, right?), which takes more time, and creates more of a risk of data becoming corrupted.
How to Delete Digital Files
Although you may think that deleting a file from your computer or network, then emptying a trash bin is sufficient, there's often more to it. Depending on the level of security you want to employ to protect the data in the old files, you may want to make sure that all the data you've deleted is overwritten with other data, or otherwise made unrecoverable. This may require defragmentation and some manual data transfers, or just hiring a tech pro you can trust.
Generally, when you delete something from your computer, even when you empty the recycle bin, the data is not lost forever. Rather, your computer essentially just tells itself that it can overwrite the data that exists in that data slot. Until it is actually overwritten, it can potentially be recovered. If you're really paranoid, there's some software you can get to make sure your deleted data is unrecoverable.