EUR/USD appears vulnerable to losses, especially given the large long position and an attractive carry appeal that favours the U.S. dollar, but there are various options that can protect and profit from further EUR/USD losses.

EUR/USD put/USD call options give holders the right to sell EUR/USD at a predetermined level and expiry date.
Of course there is a premium to pay, so option holders want EUR/USD to fall enough to cover that premium.

Options with strike further away from the current spot rate and with shorter term expiries are cheaper as there's less risk of them being exercised.
Adding a knock-out trigger below the strike will also cheapen the option, albeit limiting the profit potential.

With EUR/USD at 1.0980, a one-month expiry 1.0980 strike gives holders the right to sell EUR/USD at 1.0980 on Sept.
1 but is not cheap at 80 USD pips (break-even 1.0900).

A two-week expiry 1.0980 costs 58 pips while a two-week 1.0900 strike costs 29 pips - so profit if spot is 24 pips below the strike at expiry.

Alternatively - the initial one-month expiry 1.0980 premium can be reduced to a mere 9 USD pips by adding a knock-out trigger at 1.0800.
The option will profit if EUR/USD is below 1.0971 at expiry, but is dead if 1.0800 trades any time prior.

EUR/USD option traders are already covering downside risk.

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