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Plastic Incarnations were late-90s original audiovisual materials, re-enacting or reworking X-Files scenes by matching existing audio tracks with visuals of officially-licensed Barbie dolls. (The "plastic incarnations" of the main characters.) These short video segments were produced by a fan named BDodd, who also produced video materials for the cons she attended and appears to have been a professional or had access to professional video-editing equipment. In a period where vidding -- especially digital vidding -- was cumbersome, rare, and somewhat secretive, PIs were reasonably well-known and circulated within the fandom, and a number were included on convention souvenir videotapes, e.g. those of the OBSSE 1999 gathering.
A plastic incarnation may thus refer to an action figure that represents a fictional character, or the video made with that figure. This usage appears to be restricted almost entirely to the X-Files fandom of the late 90s.
From July 1999: "It's here! The annual OBSSE Fest Extravaganza newsletter made possible by all those wonderful Sisters and Brothers who attended this year's festivities in the thin air of Winter Park Colorado at the Beaver Village Resort. This year's FEST was a delightful gathering of 75 of the Abbey's finest and the events that took place are detailed for your enjoyment in typical irreverent OBSSE fashion. We had everything: prancing, lard, Not!videos, Scullyritas, cheese, Plastic Incarnations, games, public embarrassments, and more laughter and fun than would be possible to adequately describe. But damn it, we're gonna try. If that were not all we even had a Mulderist conversion on the last evening when our new Brother Mike realized that Scullyists just had more fun (besides if the Mulderists had a FEST we suspect they'd spend most of their time ditching each other or having holes drilled in their heads)." 
For more about "Plastic Incarnations," see "MauiGenesis: A Plastic Incarnation Travelogue Produced & Directed By: Sister Autumn Script By: Sister Paula"