= Solution
After a domain unfolds, its backbone joins the same continuous chain as previously unfolded material. The new branch differs mainly by an added <Polymer contour length>[contour length], while the local backbone bending statistics remain similar. It is therefore consistent to fit successive branches with different $L_j$ and one common $L_p\simeq0.8\,\mathrm{nm}$. <Tension>[Tension] is transmitted through serial portions of the same chain; one should not add their tensile <Force>[forces] as though they were independent parallel springs.
The <persistence length> is short compared with the contour increment per repeat, so each released domain contributes many flexible bending segments. Stretching suppresses those thermal modes and raises <Gibbs free energy>[free energy] through loss of <entropy>, which is precisely the worm-like-chain mechanism. The common $L_p$ is a property of the unfolded backbone under the measurement conditions, not the <Protein domain>[folded domain]'s axial length or the number of domains already released. With $T=300\,\mathrm K$ only as an illustrative value, $k_BT L_p\simeq3.3\,\mathrm{pN\,nm^2}$.
A common persistence-length fit is evidence for approximately repeat-independent chain flexibility over the observed branches; it is not proof that a continuum inextensible model describes every molecular scale. Residual folded structure, heterogeneous linkers, force-induced backbone stretching, and very short-chain effects can cause deviations. The formal <force> divergence at $x=L$ signals the model's inextensibility assumption, not a physical infinite tensile <force>.
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