You know, every time I see a new player come in with In Debt I sort of laugh to myself. I know they took it thinking, "I just pay cash and this is like free points." Why should In Debt be free points for just paying off in game cash? I took Day Job at 40 hours a week. OK I quit my job! Free points, yey! I took Wanted, I bought a biosculpting, now they don't know what I look like. Free points, yey! I took Borrowed Time, that player is playing a vampire. He infected me. Free points, yey!
So by your logic, really a lot of major point negative qualities could be resolved without much effort. If they get a 'free pass' then why should anyone have to pay karma to 'pay off' the extra build points in chargen?
Go read Borrowed Time again. It says that it
cannot be bought off with Karma. Period, and that if the player doesn't want the character to die, it requires the PC to burn his entire Edge attribute to survive... and even then that's at GM's Discretion.
Not to mention that, just because they've been Biosculpted, the bounty doesn't go away. If the GM can't find a way to make it stick even after the evasion tactics, they're not trying hard enough.
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Now, hyperbole aside, there are certain other Qualities that are capable of being "fixed" in game that specifically state that they must be paid off with Karma if they're corrected via roleplay... things such as High-Maintenance Implant if the implant is removed, or Nano-Intolerance if you get a Nanohive. Since there is a specific call-out on these qualities, but not on others such as In Debt, the logical conclusion is that Qualities without that call-out do not require Karma to be mitigated. The Quality would stay on the sheet, but there would be no actual effect unless future circumstances brought the Quality back into play.
Specifically, in the case of In Debt, we have the phrase "The amount owed increases 10% each month, as compound interest. If the character is unable to pay
at least the interest amount each month..." which very strongly implies they can pay against the principle. There's also no mention of having to pay Karma to do so.
If they pay the principle down to 0 the Negative Quality stays on their sheet, but there's nothing left to compound... 10% of 0 being 0 and all... so they're essentially free and clear unless/until they go back to Vinnie The Shark and take out another loan.
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In short... yes. Unless otherwise stated, a character who can Roleplay their way out of a Negative Quality does, indeed, get those so-called "free points." If a GM doesn't like it, they should disallow the Qualities in question or house-rule in the Karma cost... but that's exactly what it is, a HR.