The answer to this question depends on which interpretation of "Villanelle" you're referring to.
Villanelle (Character from Killing Eve)
In the popular BBC America television series Killing Eve, the character of Villanelle, played by Jodie Comer, is shown to have faked her death on multiple occasions. Throughout the series, she displays a talent for deception and manipulation, often using her charm and cunning to escape dangerous situations. While her fate in the final season is unclear, her history suggests that she is capable of faking her death.
Villanelle (Poem Form)
The Villanelle, as a poetic form, does not have a physical embodiment and therefore cannot "fake" its death. This poetic form, characterized by its repeating lines and specific rhyme scheme, continues to be used and enjoyed by poets today.
Conclusion
While the fictional character of Villanelle in Killing Eve is known for her ability to feign death, the Villanelle as a poetic form does not have the capacity to do so.