No worker-firm pair can break off and do better on their own. What about larger coalitions of workers and firms?
Define the total surplus any subset of workers and firms can earn for themselves. Let $S\subset\ll\cup\ff$ be a set of workers and/or firms. If $S\subset\ll$ or $S\subset\ff$ let $v_P(S)=0$. Otherwise, define the total surplus $S$ can earn for itself. \begin{equation}\label{eq:4} \begin{aligned} v_P(S)&=\max_x\sum_{l,f\in S}v_{lf}x_{lf}\\ \text{s.t.}\qquad&\begin{aligned}[c] \sum_fx_{lf}&\leq 1\text{ for all $l\in S$,}\\ \sum_lx_{lf}&\leq 1\text{ for all $f\in S$,}\\ x_{lf}&\geq0\text{ for all $l,f\in S$.} \end{aligned} \end{aligned} \end{equation} If $\sum_{l,f\in S}w_l+\pi_f< v_P(S)$, then $S$ can improve itself by breaking away.