A firm at the center of Wall Street’s plumbing is seeking $50 billion in commitments from banks and trading firms to shore up a crucial but increasingly illiquid short-term lending market, according to people familiar with the discussions.

Depository Trust & Clearing Corp wants its members to support the multibillion-dollar credit line to bolster the finances of a unit called Fixed Income Clearing Corp, which facilitates trades in the $2.6 trillion repo market, the people said.