How to retrieve actual item from HashSet<T>?

This is actually a huge omission in the set of collections. You would need either a Dictionary of keys only or a HashSet that allows for the retrieval of object references. So many people have asked for it, why it doesn't get fixed is beyond me.

Without third-party libraries the best workaround is to use Dictionary<T, T> with keys identical to values, since Dictionary stores its entries as a hash table. Performance-wise it is the same as the HashSet, but it wastes memory of course (size of a pointer per entry).

Dictionary<T, T> myHashedCollection;
...
if(myHashedCollection.ContainsKey[item])
    item = myHashedCollection[item]; //replace duplicate
else
    myHashedCollection.Add(item, item); //add previously unknown item
...
//work with unique item

What you're asking for was added to .NET Core a year ago, and was recently added to .NET 4.7.2:

In .NET Framework 4.7.2 we have added a few APIs to the standard Collection types that will enable new functionality as follows.
- ‘TryGetValue‘ is added to SortedSet and HashSet to match the Try pattern used in other collection types.

The signature is as follows (found in .NET 4.7.2 and above):

    //
    // Summary:
    //     Searches the set for a given value and returns the equal value it finds, if any.
    //
    // Parameters:
    //   equalValue:
    //     The value to search for.
    //
    //   actualValue:
    //     The value from the set that the search found, or the default value of T when
    //     the search yielded no match.
    //
    // Returns:
    //     A value indicating whether the search was successful.
    public bool TryGetValue(T equalValue, out T actualValue);

P.S.: In case you're interested, there is related function they're adding in the future - HashSet.GetOrAdd(T).

This method has been added to .NET Framework 4.7.2 (and .NET Core 2.0 before it); see HashSet<T>.TryGetValue. Citing the source:

/// <summary>
/// Searches the set for a given value and returns the equal value it finds, if any.
/// </summary>
/// <param name="equalValue">The value to search for.
/// </param>
/// <param name="actualValue">
/// The value from the set that the search found, or the default value
/// of <typeparamref name="T"/> when the search yielded no match.</param>
/// <returns>A value indicating whether the search was successful.</returns>
/// <remarks>
/// This can be useful when you want to reuse a previously stored reference instead of 
/// a newly constructed one (so that more sharing of references can occur) or to look up
/// a value that has more complete data than the value you currently have, although their
/// comparer functions indicate they are equal.
/// </remarks>
public bool TryGetValue(T equalValue, out T actualValue)