There is at least 1 phone that has that feature, the Thunderbolt has a setting in the email app that reads approximately as "sync with server" I'm assuming you're BlackBerry had the same option, when this was unchecked the emails that you downloaded to your phone would not be deleted from the phone, even after they were deleted from the server. This allowed you to have a backup copy of all of your emails always on you're phone. With the amount of memory available on the phone/sdcard this would work fine. If the setting was enabled, your phone would "mirror" your server, once the emails were downloaded to Outlook, the phone would automatically deleted them.
I don't know how the Razor works, but maybe somebody can tell you where (if there is one) that setting is.
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This backup copy on my phone is exactly what I want....I want all my emails on my phone all the time unless i specifically delete it from there.