Conversion: Cases under the Code may be converted from one chapter to another chapter; for example, a Chapter 7 case may be converted to a case under Chapter 13 if the debtor is eligible for Chapter 13. Even though the chapter of the Code which governs it changes, it remains the same case as originally filed.
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[...] a case in which assets may be liquidated, a 13 may be converted to a 7 even though debtors may not be eligible for a 7 [...]