Derby can probably get 15,000+ season ticket holders in L1, so that's perhaps £3,000,000 - £4,000,000 income, probably another £2,000,000 from match-day sales and perhaps another £1,000,000 or so from other revenue streams to give them a war chest of £6,000,000 - £8,000,000 to fund the season, and possibly they can add a bit on top from selling the players they've already got.
Since they've only got 5 players registered and most if not all of them could be on the way out, there's nothing to stop them signing up 22 trialists on £2,000 p/w each, which is going to cost a touch over £2.5m for the season, and leave plenty of headroom to cover other operating costs, maybe even pay the admin's fees.
The football might be terrible, they could end up in L2, but the only thing the EFL cares about is whether Derby has the funding in place to complete the season, if they do then they're allowed to compete.
Ultimately, the bigger the club, the easier it is to demonstrate funding, and thus the more scope for "preferential treatment" from the EFL.