How to show that sampling from correlated fraction PDFs does not reproduce correlations?

Question

Let's assume that we have $N$ layers over which a quantity X is distributed, i.e. $X = \sum_{i=1}^{N} X_i$ for each 'data point'. Now, we know how the Probability Density Function $f(X)$ of the overall quantity as well as the Probability Denity Function of the fraction in each layer $g(X_i^{\mathrm{frac}})$ with $X_i^{\mathrm{frac}}=\frac{X_i}{X}$ look. We also know that the correlations of $X_i$ are not zero, i.e. $\rho(X_i, X_j) \neq 0$. How can I concisely show that if I would just sample data from the fraction PDFs $g(X_i^{\mathrm{frac}})$ and the total PDF $f(X)$ with the constrain of the fractions always summing up to $X$, it would not be possible to reproduce the original correlations. Hope this was clear!