When a spellcaster transforms an object or creature into a creature using the True Polymorph spell, does that creature form with equipment? E.g., if a spellcaster used True Polymorph to transform a twelfth level fighter into an Erinyes, would the Erinyes form with the plate armor, magical longsword, or rope of entanglement listed in its statistics block? This isn't clear to me from True Polymorph's text, which notes the "target's game statistics, including mental ability scores, are replaced by the statistics of the new form", but doesn't address equipment.
You get all of the creature's game statistics. This includes their default equipment, powers etc (otherwise your game statistics would not be the same).
However, I think something like the alternate option such as the Rope of Entanglement would be very much at the DM's discretion. There's no clear RAW here, so it's definitely up to discretion.