ClearAll[sofncreator]
sofncreator[n_] := Module[{sample, i},
  sample = {};
  i = 0;
  Return[
   Function[{item},
    i++;
    If[i <= n,
     AppendTo[sample, item]
     ,
     If[RandomInteger[{1, i}] <= n,
      sample[[RandomInteger[{1, n}]]] = item
      ]
     ];
    sample
    ]
   ]
  ]
bin = ConstantArray[0, 10];
items = Range[10];
sofn = sofncreator[3];
Do[
 sample = sofn[item];
 Print["  Item: ", item, " -> sample: " , sample]
 ,
 {item, items}
 ]
Do[
  sofn = sofncreator[3];
  Do[
   sample = sofn[item]
   ,
   {item, items}
   ];
  Do[
   bin[[s]] += 1
   ,
   {s, sample}
   ]
  ,
  {trial, 100000}
  ];
{Range[Length[bin]], bin} // Transpose // Grid