Packing conjecture for infinite matroid families

Let $(M_k\mid k\in K)$ be a family of matroids on the same ground set $E$. A covering for $(M_k.Y\mid k\in K)$ is a family of independent sets whose union covers $Y$, and a packing is a family of pairwise disjoint spanning sets. Packing conjecture. The family $(M_k\mid k\in K)$ has a packing if and only if, for every $Y\subseteq E$, whenever $(M_k.Y\mid k\in K)$ has a covering, it also has a packing. This condition is designed as an infinite analogue of the finite base packing theorem and is stated to characterize when a packing exists.