Not exactly correct. There are circumstances in which evidence must be preserved prior to any legal claim being filed. In NJ, the standard is:
A duty to preserve evidence “arises when there is pending or likely litigation between two parties, knowledge of this fact by the alleged spoliating party, evidence relevant to the litigation, and foreseeability that the opposing party would be prejudiced by the destruction or disposal of this evidence.” Cockerline v. Menendez, 411 N.J.Super. 596, 620, 988 A.2d 575 (App.Div.) (citing Aetna Life & Cas. Co. v. Imet Mason Contractors, 309 N.J.Super. 358, 366, 707 A.2d 180 (App.Div.1998)), certif. denied, 201 N.J. 499, 992 A.2d 793 (2010).
Bldg. Materials Corp. of Am. v. Allstate Ins. Co., 424 N.J. Super. 448, 471–72, 38 A.3d 644, 658 (App. Div. 2012)(bolding added). Thus, for example, where an employer knows from the circumstances that litigation may be likely between it and an employee that may trigger the requirement to preserve evidence even prior to any litigation being filed. Note too that it is not necessary to file to move to have evidence preserved for that duty to arise; simply the filing of the litigation would do that even if the duty did not arise before the litigation started.
Destruction of evidence that should have been preserved is known in the law as spoliation. If spoliation can be proven there are a variety of remedies for that depending on when the spoliation was discovered.
I agree that's a good idea.