Preparation of Grignard reagent. Free radical rearrangement
Grignard reagent is an organomagnesium halide in which magnesium and halide bond is ionic. It is not like magnesium is always inserted in between carbon and halogen bond. Once formed, magnesium-carbon bond should be configurationally stable under the conditions of the reaction (Ref.1), and is polar covalent (at least partially) so that $\ce{Mg}$ has to be connected to its bonding partner $\ce{C}$ in the first place. In this polar covalent bond, carbon ends up being the negative end of the dipole, giving its nucleophilicity. The reaction undergoes in free radical mechanism (yet it does not involve a radical chain mechanism) to form Grignard reagent:
$$\ce{R-X + ^.Mg^. -&gt;[\text{r.d.s.}] R^. + ^.Mg+X-} \tag1$$
$$\ce{R^. + ^.Mg+X- -&gt; R-Mg+X-} \tag2$$
Magnesium metal has two valance electrons. The first step is the rate-determining step in this two-step mechanism, which happens on the surface of the metal. In this first step, $\ce{Mg}$ metal transfers one of its two valance electrons to the halogen radical, cleaving carbon-halogen bond homolytically. The process in step by step mode to explain the outcome:
$$\ce{R-X -&gt; [R^. + X^.] -&gt;[^.Mg^.] R^. + ^.Mg+X-} \tag3$$
This first step forms two radicals: $\ce{^.Mg+}$ and $\ce{R^.}$. These two radicals then get terminated by coupling each other to give the Grignard reagent in second step. The rearrangement of $\ce{R^.}$ (if there any) during the second step depends on the rate of rearrangement compared to the rate of the radical termination. However, according to the Ref.1, both chiral cyclopropyl-magnesium bond and vinyl-magnesium bond do in fact retain their configurations from parent alkyl halides. The authors carefully chose non-ionizable alkyl halide in solvent for this study so that any rearrangement should happen during the reaction (e.g., cyclopropyl tosylate solvolyzes at a rate of $\pu{5.7 \times 10^{-13} s-1}$ in actic acid at $\pu{25 ^\circ C}$, Ref.2). The excistence of $\ce{R^.}$ intermediate is proven by trapping it using $\ce{TEMPO^.}$ radical (Ref.3).
References:

H. M. Walborsky, &quot;Mechanism of Grignard reagent formation. The surface nature of the reaction,&quot; Acc. Chem. Res. 1990, 23(9), 286–293 (https://doi.org/10.1021/ar00177a004).
P. von R. Schleyer, W. F. Sliwinski, G. W. Van Dine, U. Schöellkopf, J. Paust, K. Fellenberger, &quot;Cyclopropyl solvolyses. III. Parent cyclopropyl derivatives and methyl-substituted cyclopropyl tosylates,&quot; J. Am. Chem. Soc. 1972, 94(1), 125–133 (https://doi.org/10.1021/ja00756a024).
Karen S. Root, Craig L. Hill, Lynette M. Lawrence, George M. Whitesides, &quot;The mechanism of formation of Grignard reagents: trapping of free alkyl radical intermediates by reaction with tetramethylpiperidine-N-oxyl,&quot; J. Am. Chem. Soc. 1989, 111(14), 5405–5412 (https://doi.org/10.1021/ja00196a053).